TTTTTaaaaabbbbbllllleeeee 1111111111.....2222200000
CCCCCooooommmmmpppppuuuuutttttaaaaatttttiiiiiooooonnnnn ooooofffff ttttthhhhheeeee OOOOOrrrrriiiiigggggiiiiinnnnnaaaaalllll FFFFFrrrrreeeeeqqqqquuuuueeeeennnnncccccyyyyy DDDDDiiiiissssstttttrrrrriiiiibbbbbuuuuutttttiiiiiooooonnnnn
x = class interval
i
C
d f 55 + 2d x ±
i i i i 2
–2 17 51 50-52
–1 35 53 52-54
0 28 55 54-56
1 15 57 56-58
2 5 59 58-60
EEEEExxxxxaaaaammmmmpppppllllleeeee 1111111111.....4444455555::::: Compute coefficient of variation from the following data:
Age : under 10 under 20 under 30 under 40 under 50 under 60
No. of persons
Dying : 10 18 30 45 60 80
SSSSSooooollllluuuuutttttiiiiiooooonnnnn::::: What is given in this problem is less than cumulative frequency distribution. We
need first convert it to a frequency distribution and then compute the coefficient of variation.
TTTTTaaaaabbbbbllllleeeee 1111111111.....2222211111
CCCCCooooommmmmpppppuuuuutttttaaaaatttttiiiiiooooonnnnn ooooofffff cccccoooooeeeeeffffffffffiiiiiccccciiiiieeeeennnnnttttt ooooofffff vvvvvaaaaarrrrriiiiiaaaaatttttiiiiiooooonnnnn
Age in years No. of persons Mid-value d
i
class Interval dying x –25 fd fd2
i i i i i
(f) (x) 10
i i
0-10 10 5 –2 –20 40
10-20 18–10= 8 15 –1 –8 8
20-30 30–18=12 25 0 0 0
30-40 45–30=15 35 1 15 15
40-50 60–45=15 45 2 30 60
50-60 80–60=20 55 3 60 180
Total 80 – – 77 303
(cid:19)(cid:5)(cid:3)(cid:5)(cid:17)(cid:19)(cid:5)(cid:17)(cid:1)(cid:19) (cid:10)(cid:10)(cid:11)(cid:22)(cid:10)
Copyright -The Institute of Chartered Accountants of India
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4)(cid:7)(cid:8)(cid:9)(cid:7)(cid:10)(cid:2)(cid:11)(cid:12)(cid:6)(cid:3)(cid:13)(cid:7)(cid:12)(cid:2)(cid:11)(cid:14)(cid:2)(cid:11)(cid:10)(cid:15)(cid:7)(cid:3)(cid:11)(cid:14)(cid:7)(cid:14)(cid:16)(cid:4)(cid:17)(cid:2)(cid:6)(cid:4)(cid:16)(cid:8)(cid:11)
The AM is given by:
∑fd
x = A+ i i×C
N
77
=
25+ ×10
years
80
= 34.63 years
The standard deviation is
∑fd2 ∑fd 2
s = i i − i i ×C
N N
303 77 2
= − ×10years
80 80
= (cid:5)(cid:3)(cid:16)(cid:14) − (cid:21)(cid:3)(cid:14)(cid:5) × (cid:7)(cid:21)(cid:25)(cid:26)!(cid:30)4(cid:28)
= 16.91 years
Thus the coefficient of variation is given by
,
5 (cid:7)(cid:21)(cid:21)
= (cid:2)×
(cid:7)(cid:20)(cid:3)(cid:14)(cid:7)
(cid:7)(cid:21)(cid:21)
= ×
(cid:5)(cid:19)(cid:3)(cid:20)(cid:5)
= 48.83
EEEEExxxxxaaaaammmmmpppppllllleeeee 1111111111.....4444466666 ::::: you are given the distribution of wages in two factors A and B
Wages in Rs. : 100-200 200-300 300-400 400-500 500-600 600-700
No. of
workers in A : 8 12 17 10 2 1
No. of
workers in B : 6 18 25 12 2 2
State in which factory, the wages are more variable.
Solution :
As explained in example 11.36, we need compare the coefficient of variation of A(i.e. v ) and
A
of B (i.e v ).
B
If v > v , then the wages of factory A would be more variable. Otherwise, the wages of factory
A B
B would be more variable where
s s
V =100× A V =100× B
and
A x B x
A B
(cid:10)(cid:10)(cid:11)(cid:22)(cid:12) (cid:1)(cid:13)(cid:14)(cid:14)(cid:13)(cid:15)(cid:8) (cid:4)(cid:7)(cid:13)(cid:16)(cid:17)(cid:1)(cid:17)(cid:6)(cid:15)(cid:1)(cid:18)(cid:8) (cid:5)(cid:6)(cid:19)(cid:5)
Copyright -The Institute of Chartered Accountants of India
TTTTTaaaaabbbbbllllleeeee 1111111111.....2222222222
CCCCCooooommmmmpppppuuuuutttttaaaaatttttiiiiiooooonnnnn ooooofffff cccccoooooeeeeeffffffffffiiiiiccccciiiiieeeeennnnnttttt ooooofffff vvvvvaaaaarrrrriiiiiaaaaatttttiiiiiooooonnnnn ooooofffff wwwwwaaaaagggggeeeeesssss ooooofffff TTTTTwwwwwooooo FFFFFaaaaaccccctttttooooorrrrriiiiieeeeesssss AAAAA aaaaannnnnddddd BBBBB
Wages Mid-value d= No. of workers No. of workers
in rupees x of A of B f d f d2 fd f d2
A A B B
f f
A B
(1) (2) (3) (4) (5) (6)=(3)×(4) (7)=(3)×(6) (8)=(3)×(5) (9)=(3)×(8)
100-200 150 –2 8 6 –16 32 –12 24
200-300 250 –1 12 18 –12 12 –18 18
300-400 350 0 17 25 0 0 0 0
400-500 450 1 10 12 10 10 12 12
500-600 550 2 2 2 4 8 4 8
600-700 650 3 1 2 3 9 6 18
Total – – 50 65 –11 71 – 8 80
For Factory A
−11
x =Rs. 350+ ×100 =Rs.328
A 50
(cid:16)(cid:7) ((cid:24)(cid:7)(cid:7))(cid:6)
, (cid:27)(cid:28)(cid:3) (cid:7)(cid:21)(cid:21) (cid:25)(cid:25)(cid:27)(cid:28)(cid:3)(cid:25)(cid:7)(cid:7)(cid:16)(cid:3)(cid:7)(cid:6)
= − × =
(cid:12) (cid:17)(cid:21) (cid:17)(cid:21)
,
5 (cid:12) (cid:7)(cid:21)(cid:21) (cid:5)(cid:17)(cid:3)(cid:16)(cid:7)
∴ (cid:12) = (cid:2) × =
(cid:12)
For Factory B
( (cid:18) )
(cid:2) (cid:27)(cid:28)(cid:3)(cid:5)(cid:17)(cid:21) − (cid:7)(cid:21)(cid:21) (cid:27)(cid:28)(cid:3)(cid:5)(cid:5)(cid:16)(cid:3)(cid:20)(cid:14)
= + × =
2 (cid:20)(cid:17)
(cid:18)(cid:21) ( (cid:18))(cid:6)
, (cid:27)(cid:28)(cid:3) − (cid:7)(cid:21)(cid:21)
= − ×
2 (cid:20)(cid:17) (cid:20)(cid:17)
= Rs.110.25
110.25
∴V = ×100 = 32.65
B 337.69
As V > V , the wages for factory A is more variable.
A B
(cid:19)(cid:5)(cid:3)(cid:5)(cid:17)(cid:19)(cid:5)(cid:17)(cid:1)(cid:19) (cid:10)(cid:10)(cid:11)(cid:22)(cid:20)
Copyright -The Institute of Chartered Accountants of India
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4)(cid:7)(cid:8)(cid:9)(cid:7)(cid:10)(cid:2)(cid:11)(cid:12)(cid:6)(cid:3)(cid:13)(cid:7)(cid:12)(cid:2)(cid:11)(cid:14)(cid:2)(cid:11)(cid:10)(cid:15)(cid:7)(cid:3)(cid:11)(cid:14)(cid:7)(cid:14)(cid:16)(cid:4)(cid:17)(cid:2)(cid:6)(cid:4)(cid:16)(cid:8)(cid:11)
CCCCCooooommmmmpppppaaaaarrrrriiiiisssssooooonnnnn bbbbbeeeeetttttwwwwweeeeeeeeeennnnn dddddiiiiiffffffffffeeeeerrrrreeeeennnnnttttt mmmmmeeeeeaaaaasssssuuuuurrrrreeeeesssss ooooofffff dddddiiiiissssspppppeeeeerrrrrsssssiiiiiooooonnnnn
We may now have a review of the different measures of dispersion on the basis of their relative
merits and demerits. Standard deviation, like AM, is the best measure of dispersion. It is rigidly
defined, based on all the observations, not too difficult to compute, not much affected by
sampling fluctuations and moreover it has some desirable mathematical properties. All these
merits of standard deviation make SD as the most widely and commonly used measure of
dispersion.
Range is the quickest to compute and as such, has its application in statistical quality control.
However, range is based on only two observations and affected too much by the presence of
extreme observation(s).
Mean deviation is rigidly defined, based on all the observations and not much affected by
sampling fluctuations. However, mean deviation is difficult to comprehend and its computation
is also time consuming and laborious. Furthermore, unlike SD, mean deviation does not possess
mathematical properties.
Quartile deviation is also rigidly defined, easy to compute and not much affected by sampling
fluctuations. The presence of extreme observations has no impact on quartile deviation since
quartile deviation is based on the central fifty-percent of the observations. However, quartile
deviation is not based on all the observations and it has no desirable mathematical properties.
Nevertheless, quartile deviation is the best measure of dispersion for open-end classifications.
1111111111.....1111133333 EEEEEXXXXXEEEEERRRRRCCCCCIIIIISSSSSEEEEE
SSSSSeeeeettttt AAAAA
WWWWWrrrrriiiiittttteeeee dddddooooowwwwwnnnnn ttttthhhhheeeee cccccooooorrrrrrrrrreeeeecccccttttt aaaaannnnnssssswwwwweeeeerrrrrsssss..... EEEEEaaaaaccccchhhhh qqqqquuuuueeeeessssstttttiiiiiooooonnnnn cccccaaaaarrrrrrrrrriiiiieeeeesssss ooooonnnnneeeee mmmmmaaaaarrrrrkkkkk.....
1. Which of the following statements is correct?
(a) Two distributions may have identical measures of central tendency and dispersion.
(b) Two distributions may have the identical measures of central tendency but different
measures of dispersion.
(c) Two distributions may have the different measures of central tendency but identical
measures of dispersion.
(d) All the statements (a), (b) and (c).
2. Dispersion measures
(a) The scatterness of a set of observations
(b) The concentration of a set of observations
(c) Both a) and b)
(d) Neither a) and b).
(cid:10)(cid:10)(cid:11)(cid:22)(cid:21) (cid:1)(cid:13)(cid:14)(cid:14)(cid:13)(cid:15)(cid:8) (cid:4)(cid:7)(cid:13)(cid:16)(cid:17)(cid:1)(cid:17)(cid:6)(cid:15)(cid:1)(cid:18)(cid:8) (cid:5)(cid:6)(cid:19)(cid:5)
Copyright -The Institute of Chartered Accountants of India
3. When it comes to comparing two or more distributions we consider
(a) Absolute measures of dispersion (b) Relative measures of dispersion
(c) Both a) and b) (d) Either (a) or (b).
4. Which one is difficult to compute?
(a) Relative measures of dispersion (b) Absolute measures of dispersion
(c) Both a) and b) (d) Range
5. Which one is an absolute measure of dispersion?
(a) Range (b) Mean Deviation
(c) Standard Deviation (d) All these measures
6. Which measure of dispersion is the quickest to compute?
(a) Standard deviation (b) Quartile deviation
(c) Mean deviation (d) Range
7. Which measures of dispersions is not affected by the presence of extreme observations?
(a) Range (b) Mean deviation
(c) Standard deviation (d) Quartile deviation
8. Which measure of dispersion is based on the absolute deviations only?
(a) Standard deviation (b) Mean deviation
(c) Quartile deviation (d) Range
9. Which measure is based on only the central fifty percent of the observations?
(a) Standard deviation (b) Quartile deviation
(c) Mean deviation (d) All these measures
10. Which measure of dispersion is based on all the observations?
(a) Mean deviation (b) Standard deviation
(c) Quartile deviation (d) (a) and (b) but not (c)
11. The appropriate measure of dispersions for open – end classification is
(a) Standard deviation (b) Mean deviation
(c) Quartile deviation (d) All these measures.
12. The most commonly used measure of dispersion is
(a) Range (b) Standard deviation
(c) Coefficient of variation (d) Quartile deviation.
(cid:19)(cid:5)(cid:3)(cid:5)(cid:17)(cid:19)(cid:5)(cid:17)(cid:1)(cid:19) (cid:10)(cid:10)(cid:11)(cid:22)(cid:22)
Copyright -The Institute of Chartered Accountants of India
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4)(cid:7)(cid:8)(cid:9)(cid:7)(cid:10)(cid:2)(cid:11)(cid:12)(cid:6)(cid:3)(cid:13)(cid:7)(cid:12)(cid:2)(cid:11)(cid:14)(cid:2)(cid:11)(cid:10)(cid:15)(cid:7)(cid:3)(cid:11)(cid:14)(cid:7)(cid:14)(cid:16)(cid:4)(cid:17)(cid:2)(cid:6)(cid:4)(cid:16)(cid:8)(cid:11)
13. Which measure of dispersion has some desirable mathematical properties?
(a) Standard deviation (b) Mean deviation
(c) Quartile deviation (d) All these measures
14. If the profits of a company remains the same for the last ten months, then the standard
deviation of profits for these ten months would be ?
(a) Positive (b) Negative (c) Zero (d) (a) or (c)
15. Which measure of dispersion is considered for finding a pooled measure of dispersion
after combining several groups?
(a) Mean deviation (b) Standard deviation
(c) Quartile deviation (d) Any of these
16. A shift of origin has no impact on
(a) Range (b) Mean deviation
(c) Standard deviation (d) All these and quartile deviation.
17. The range of 15, 12, 10, 9, 17, 20 is
(a) 5 (b) 12 (c) 13 (d) 11.
18. The standard deviation of, 10, 16, 10, 16, 10, 10, 16, 16 is
(a) 4 (b) 6 (c) 3 (d) 0.
19. For any two numbers SD is always
(a) Twice the range (b) Half of the range
(c) Square of the range (d) None of these.
20. If all the observations are increased by 10, then
(a) SD would be increased by 10
(b) Mean deviation would be increased by 10
(c) Quartile deviation would be increased by 10
(d) All these three remain unchanged.
21. If all the observations are multiplied by 2, then
(a) New SD would be also multiplied by 2
(b) New SD would be half of the previous SD
(c) New SD would be increased by 2
(d) New SD would be decreased by 2.
(cid:10)(cid:10)(cid:11)(cid:22)(cid:23) (cid:1)(cid:13)(cid:14)(cid:14)(cid:13)(cid:15)(cid:8) (cid:4)(cid:7)(cid:13)(cid:16)(cid:17)(cid:1)(cid:17)(cid:6)(cid:15)(cid:1)(cid:18)(cid:8) (cid:5)(cid:6)(cid:19)(cid:5)
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SSSSSeeeeettttt BBBBB
WWWWWrrrrriiiiittttteeeee dddddooooowwwwwnnnnn ttttthhhhheeeee cccccooooorrrrrrrrrreeeeecccccttttt aaaaannnnnssssswwwwweeeeerrrrrsssss..... EEEEEaaaaaccccchhhhh qqqqquuuuueeeeessssstttttiiiiiooooonnnnn cccccaaaaarrrrrrrrrriiiiieeeeesssss tttttwwwwwooooo mmmmmaaaaarrrrrkkkkksssss.....
1. What is the coefficient of range for the following wages of 8 workers?
Rs.80, Rs.65, Rs.90, Rs.60, Rs.75, Rs.70, Rs.72, Rs.85.
(a) Rs.30 (b) Rs.20 (c) 30 (d) 20
2. If R and R denote ranges of x and y respectively where x and y are related by 3x+2y+10=0,
x y
what would be the relation between x and y?
(a) R = R (b) 2 R = 3 R (c) 3 R = 2 R (d) R = 2 R
x y x y x y x y
3. What is the coefficient of range for the following distribution?
Class Interval : 10-19 20-29 30-39 40-49 50-59
Frequency : 11 25 16 7 3
(a) 22 (b) 50 (c) 72.46 (d) 75.82
4. If the range of x is 2, what would be the range of –3x +50 ?
(a) 2 (b) 6 (c) –6 (d) 44
5. What is the value of mean deviation about mean for the following numbers?
5, 8, 6, 3, 4.
(a) 5.20 (b) 7.20 (c) 1.44 (d) 2.23
6. What is the value of mean deviation about mean for the following observations?
50, 60, 50, 50, 60, 60, 60, 50, 50, 50, 60, 60, 60, 50.
(a) 5 (b) 7 (c) 35 (d) 10
7. The coefficient of mean deviation about mean for the first 9 natural numbers is
(a) 200/9 (b) 80 (c) 400/9 (d) 50.
8. If the relation between x and y is 5y–3x = 10 and the mean deviation about mean for x is
12, then the mean deviation of y about mean is
(a) 7.20 (b) 6.80 (c) 20 (d) 18.80.
9. If two variables x and y are related by 2x + 3y –7 =0 and the mean and mean deviation
about mean of x are 1 and 0.3 respectively, then the coefficient of mean deviation of y
about mean is
(a) –5 (b) 12 (c) 50 (d) 4.
10. The mean deviation about mode for the numbers 4/11, 6/11, 8/11, 9/11, 12/11, 8/11 is
(a) 8/11 (b) 1 (c) 6/11 (d) 5/11.
11. What is the standard deviation of 5, 5, 9, 9, 9, 10, 5, 10, 10?
(a) 14 (b) 42 (c) 4.50 (d) 8
(cid:19)(cid:5)(cid:3)(cid:5)(cid:17)(cid:19)(cid:5)(cid:17)(cid:1)(cid:19) (cid:10)(cid:10)(cid:11)(cid:22)(cid:24)
Copyright -The Institute of Chartered Accountants of India
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4)(cid:7)(cid:8)(cid:9)(cid:7)(cid:10)(cid:2)(cid:11)(cid:12)(cid:6)(cid:3)(cid:13)(cid:7)(cid:12)(cid:2)(cid:11)(cid:14)(cid:2)(cid:11)(cid:10)(cid:15)(cid:7)(cid:3)(cid:11)(cid:14)(cid:7)(cid:14)(cid:16)(cid:4)(cid:17)(cid:2)(cid:6)(cid:4)(cid:16)(cid:8)(cid:11)
x–a
12. If the mean and SD of x are a and b respectively, then the SD of is
b
(a) –1 (b) 1 (c) ab (d) a/b.
13. What is the coefficient of variation of the following numbers?
53, 52, 61, 60, 64.
(a) 8.09 (b) 18.08 (c) 20.23 (d) 20.45
14. If the SD of x is 3, what us the variance of (5–2x)?
(a) 36 (b) 6 (c) 1 (d) 9
15. If x and y are related by 2x+3y+4 = 0 and SD of x is 6, then SD of y is
(a) 22 (b) 4 (c) 5 (d) 9.
16. The quartiles of a variable are 45, 52 and 65 respectively. Its quartile deviation is
(a) 10 (b) 20 (c) 25 (d) 8.30.
17. If x and y are related as 3x+4y = 20 and the quartile deviation of x is 12, then the quartile
deviation of y is
(a) 16 (b) 14 (c) 10 (d) 9.
18. If the SD of the 1st n natural numbers is 2, then the value of n must be
(a) 2 (b) 7 (c) 6 (d) 5.
19. If x and y are related by y = 2x+ 5 and the SD and AM of x are known to be 5 and 10
respectively, then the coefficient of variation is
(a) 25 (b) 30 (c) 40 (d) 20.
20. The mean and SD for a, b and 2 are 3 and 1 respectively, The value of ab would be
(a) 5 (b) 6 (c) 12 (d) 3.
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Write down the correct answer. Each question carries 5 marks.
1. What is the mean deviation about mean for the following distribution?
Variable : 5 10 15 20 25 30
Frequency: 3 4 6 5 3 2
(a) 6.00 (b) 5.93 (c) 6.07 (d) 7.20
(cid:10)(cid:10)(cid:11)(cid:22)(cid:25) (cid:1)(cid:13)(cid:14)(cid:14)(cid:13)(cid:15)(cid:8) (cid:4)(cid:7)(cid:13)(cid:16)(cid:17)(cid:1)(cid:17)(cid:6)(cid:15)(cid:1)(cid:18)(cid:8) (cid:5)(cid:6)(cid:19)(cid:5)
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2. What is the mean deviation about median for the following data?
X : 3 5 7 9 11 13 15
F : 2 8 9 16 14 7 4
(a) 2.50 (b) 2.46 (c) 2.43 (d) 2.37
3. What is the coefficient of mean deviation for the following distribution of height? Take
deviation from AM.
Height in inches: 60-62 63-65 66-68 69-71 72-74
No. of students: 5 22 28 17 3
(a) 2.30 inches (b) 3.45 (c) 3.82 (d) 2.48 inches
4. The mean deviation of weight about median for the following data:
Weight (lb) : 131-140 141-150 151-160 161-170 171-180 181-190
No. of persons : 3 8 13 15 6 5
Is given by
(a) 10.97 (b) 8.23 (c) 9.63 (d) 11.45.
5. What is the standard deviation from the following data relating to the age distribution of
200 persons?
Age (year) : 20 30 40 50 60 70 80
No. of people: 13 28 31 46 39 23 20
(a) 15.29 (b) 16.87 (c) 18.00 (d) 17.52
6. What is the coefficient of variation for the following distribution of wages?
Daily Wages (Rs.) 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80 80 – 90
No. of workers 17 28 21 15 13 6
(a) Rs.14.73 (b) 14.73 (c) 26.93 (d) 20.82
7. Which of the following companies A and B is more consistent so far as the payment of
dividend are concerned ?
Dividend paid by A : 5 9 6 12 15 10 8 10
Dividend paid by B : 4 8 7 15 18 9 6 6
(a) A (b) B (c) Both (a) and (b) (d) Neither (a) nor (b)
8. The mean and SD for a group of 100 observations are 65 and 7.03 respectively. If 60 of
these observations have mean and SD as 70 and 3 respectively, what is the SD for the
group comprising 40 observations?
(a) 16 (b) 25 (c) 4 (d) 2
9. If two samples of sizes 30 and 20 have means as 55 and 60 and variances as 16 and 25
respectively, then what would be the SD of the combined sample of size 50?
(a) 5.00 (b) 5.06 (c) 5.23 (d) 5.35
(cid:19)(cid:5)(cid:3)(cid:5)(cid:17)(cid:19)(cid:5)(cid:17)(cid:1)(cid:19) (cid:10)(cid:10)(cid:11)(cid:22)(cid:26)
Copyright -The Institute of Chartered Accountants of India
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4)(cid:7)(cid:8)(cid:9)(cid:7)(cid:10)(cid:2)(cid:11)(cid:12)(cid:6)(cid:3)(cid:13)(cid:7)(cid:12)(cid:2)(cid:11)(cid:14)(cid:2)(cid:11)(cid:10)(cid:15)(cid:7)(cid:3)(cid:11)(cid:14)(cid:7)(cid:14)(cid:16)(cid:4)(cid:17)(cid:2)(cid:6)(cid:4)(cid:16)(cid:8)(cid:11)
10. The mean and SD of a sample of 100 observations were calculated as 40 and 5.1 respectively
by a CA student who took one observation as 50 instead of 40 by mistake. The current
value of SD would be
(a) 4.90 (b) 5.00 (c) 4.88 (d) 4.85.
11. The value of appropriate measure of dispersion for the following distribution of daily
wages
Wages (Rs.) : Below 30 30-39 40-49 50-59 60-79 Above 80
No. of workers 5 7 18 32 28 10
is given by
(a) Rs.11.03 (b) Rs.10.50 (c) 11.68 (d) Rs.11.68.
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1 (d) 2 (a) 3 (b) 4 (a) 5 (d) 6 (d)
7 (d) 8 (b) 9 (b) 10 (d) 11 (c) 12 (b)
13 (a) 14 (c) 15 (b) 16 (d) 17 (d) 18 (c)
19 (b) 20 (d) 21 (a)
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1 (d) 2 (c) 3 (c) 4 (b) 5 (c) 6 (c)
7 (c) 8 (a) 9 (b) 10 (b) 11 (b) 12 (b)
13 (a) 14 (a) 15 (b) 16 (a) 17 (d) 18 (b)
19 (c) 20 (a)
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1 (c) 2 (d) 3 (b) 4 (a) 5 (b) 6 (c)
7 (a) 8 (c) 9 (b) 10 (b) 11 (a)
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1. The no. of measures of central tendency is
(a) two (b) three (c) four (d) five
2. The words “mean” or “average” only refer to
(a) A.M (b) G.M (c) H.M (d) none
3. —————— is the most stable of all the measures of central tendency.
(a) G.M (b) H.M (c) A.M (d) none.
4. Mean is of ———— types.
(a) 3 (b) 4 (c) 8 (d) 5
5. Weighted A.M is related to
(a) G.M (b) frequency (c) H.M (d) none.
6. Frequencies are also called weights.
(a) True (b) false (c) both (d) none
7. The algebraic sum of deviations of observations from their A.M is
(a) 2 (b) -1 (c) 1 (d) 0
8. G.M of a set of n observations is the ———— root of their product.
(a) n/2 th (b) (n+1)th (c) nth (d) (n -1)th
9. The algebraic sum of deviations of 8,1,6 from the A.M viz.5 is
(a) -1 (b) 0 (c) 1 (d) none
10. G.M of 8, 4,2 is
(a) 4 (b) 2 (c) 8 (d) none
11. ——————— is the reciprocal of the A.M of reciprocal of observations.
(a) H.M (b) G.M (c) both (d) none
12. A.M is never less than G.M
(a). True (b) false (c) both (d) none
13. G.M is less than H.M
(a) true (b) false (c) both (d) none
14. The value of the middlemost item when they are arranged in order of magnitude is called
(a) standard deviation (b) mean (c) mode (d) median
15. Median is unaffected by extreme values.
(a) true (b) false (c) both (d) none
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16. Median of 2,5,8,4,9,6,71 is
(a) 9 (b) 8 (c) 5 (d) 6
17. The value which occurs with the maximum frequency is called
(a) median (b) mode (c) mean (d) none
18. In the formula Mode = L + (d X c)/ (d + d )
1 1 1 2
d is the difference of frequencies in the modal class & the —————— class.
1
(a) preceding (b) following (c) both (d) none
19. In the formula Mode = L + (d X c)/ (d + d )
1 1 1 2
d is the difference of frequencies in the modal class & the ———————— class.
2
(a) preceding (b) following (c) both (d) none
20. In formula of median for grouped frequency distribution N is
(a) total frequency (b) frequency density
(c) frequency (d) cumulative frequency
21. When all observations occur with equal frequency ————— does not exit.
(a) median (b) mode (c) mean (d) none
22. Mode of the observations 2,5,8,4,3,4,4,5,2,4,4 is
(a) 3 (b) 2 (c) 5 (d) 4
23. For the observations 5,3,6,3,5,10,7,2 , there are —————— modes.
(a) 2 (b) 3 (c) 4 (d) 5
24. —————— of a set of observations is defined to be their sum, divided by the no. of
observations.
(a) H.M (b) G.M (c) A.M (d) none
25. Simple average is sometimes called
(a) weighted average (b) unweighted average
(c) relative average (d) none
26. When a frequency distribution is given, the frequencies of values are themselves treated as
weights.
(a) True (b) false (c) both (d) none
27. Each different value is considered only once for
(a) simple average (b) weighted average
(c) both (d) none
28. Each value is considered as many times as it occurs for
(a) simple average (b) weighted average
(c) both (d) none
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29. Multiplying the values of the variable by the corresponding weights and then dividing the
sum of products by the sum of weights is
(a) simple average (b) weighted average
(c) both (d) none
30. Simple & weighted average are equal only when all the weights are equal.
(a) True (b) false (c) both (d) none
31. The word “ average “ used in “simple average “ and “weighted average “ generally refers
to
(a) median (b) mode (c) A.M , G.M or H.M (d) none
32. —————— average is obtained on dividing the total of a set of observations by their no.
(a) simple (b) weighted (c) both (d) none
33. Frequencies are generally used as
(a) range (b) weights (c) mean (d) none
34. The total of a set of observations is equal to the product of their no. and the
(a) A.M (b) G.M (c) A.M (d) none
35. The total of the deviations of a set of observations from their A.M is always
(a) 0 (b) 1 (c) -1 (d) none
36. Deviation may be positive or negative or zero
(a) true (b) false (c) both (d) none
37. The sum of the squares of deviations of a set of observations has the smallest value, when
the deviations are taken from their
(a) A.M (b) H.M (c) G.M (d) none
38. For a given set of observations H.M is less than G.M
(a) true (b) false (c) both (d) none
39. For a given set of observations A.M is greater than G.M
(a) true (b) false (c) both (d) none
40. Calculation of G.M is more difficult than
(a) A.M (b) H.M (c) median (d) none
41. ————— has a limited use
(a) A.M (b) G.M (c) H.M (d) none
42. A.M of 8,1,6 is
(a) 5 (b) 6 (c) 4 (d) none
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43. ————— can be calculated from a frequency distribution with open end intervals
(a) Median (b) Mean (c) Mode (d) none
44. The values of all items are taken into consideration in the calculation of
(a) median (b) mean (c) mode (d) none
45. The values of extreme items do not influence the average in case of
(a) median (b) mean (c) mode (d) none
46. In a distribution with a single peak and moderate skewness to the right, it is closer to the
concentration of the distribution in case of
(a) mean (b) median (c) both (d) none
47. If the variables x & z are so related that z = ax + b for each x = x where a & b are
i
constants, then z bar = ax bar + b
(a) true (b) false (c) both (d) none
48. G.M is defined only when
(a) all observations have the same sign and none is zero
(b) all observations have the different sign and none is zero
(c) all observations have the same sign and one is zero
(d) all observations have the different sign and one is zero
49. ———— is useful in averaging ratios, rates and percentages.
(a) A.M (b) G.M (c) H.M (d) none
50. G.M is useful in construction of index number.
(a) true (b) false (c) both (d) none
51. More laborious numerical calculations involves in G.M than A.M
(a) True (b) false (c) both (d) none
52. H.M is defined when no observation is
(a) 3 (b) 2 (c) 1 (d) 0
53. When all values occur with equal frequency, there is no
(a) mode (b) mean (c) median (d) none
54. ———— cannot be treated algebraically
(a) mode (b) mean (c) median (d) none
55. For the calculation of ————— , the data must be arranged in the form of a frequency
distribution.
(a) median (b) mode (c) mean (d) none
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56. ———— is equal to the value corresponding to cumulative frequency
(a) mode (b) mean (c) median (d) none
57. ————— is the value of the variable corresponding to the highest frequency
(a) mode (b) mean (c) median (d) none
58. The class in which mode belongs is known as
(a) median class (b) mean class (c) modal class (d) none
59. The formula of mode is applicable if classes are of ————— width.
(a) equal (b) unequal (c) both (d) none
60. For calculation of ——— we have to construct cumulative frequency distribution
(a) mode (b) median (c) mean (d) none
61. For calculation of ——— we have to construct a grouped frequency distribution
(a) median (b) mode (c) mean (d) none
62. Relation between mean, median & mode is
(a) mean - mode = 2 (mean—median) (b) mean - median = 3 ( mean—mode)
(c) mean - median = 2 (mean—mode) (d) mean - mode = 3 ( mean—median)
63. When the distribution is symmetrical, mean, median and mode
(a) coincide (b) do not coincide (c) both (d) none
64. Mean, median & mode are equal for the
(a) Binomial distribution (b) Normal distribution
(c) both (d) none
65. In most frequency distributions, it has been observed that the three measures of central
tendency viz.mean , median & mode ,obey the approximate relation , provided the
distribution is
(a) very skew (b) not very skew (c) both (d) none
66. —————— divides the total no. of observations into two equal parts.
(a) mode (b) mean (c) median (d) none
67. Measures which are used to divide or partition, the observations into a fixed no. of parts
are collectively known as
(a) partition values (b) quartiles (c) both (d) none
68. The middle most value of a set of observations is
(a) median (b) mode (c) mean (d) none
69. The no. of observations smaller than ———— is the same as the no. larger than it.
(a) median (b) mode (c) mean (d) none
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70. ———— is the value of the variable corresponding to cumulative frequency N /2
(a) mode (b) mean (c) median (d) none
71. ——————— divide the total no. observations into 4 equal parts.
(a) median (b) deciles (c) quartiles (d) percentiles
72. ——————— quartile is known as Upper quartile
(a) First (b) Second (c) Third (d) none
73. Lower quartile is
(a) first quartile (b) second quartile (c) upper quartile (d) none
74. The no. of observations smaller than lower quartile is the same as the no. lying between
lower and middle quartile.
(a) true (b) false (c) both (d) none
75. ———— are used for measuring central tendency, dispersion & skewness.
(a) Median (b) Deciles (c) Percentiles (d) Quartiles.
76. The second quartile is known as
(a) median (b) lower quartile (c) upper quartile (d) none
77. The lower & upper quartiles are used to define
(a) standard deviation (b) quartile deviation
(c) both (d) none
78. Three quartiles are used in
(a) Pearson' s formula (b) Bowley' s formula
(c) both (d) none
79. Less than First quartile , the frequency is equal to
(a) N /4 (b) 3N /4 (c) N /2 (d) none
80. Between first & second quartile, the frequency is equal to
(a) 3N/4 (b) N /2 (c) N /4 (d) none
81. Between second & upper quartile, the frequency is equal to
none
a) 3N/4 (b) N /4 ( c) N /2 (d)
82. Above upper quartile, the frequency is equal to
(a) N /4 (b) N /2 (c) 3N /4 (d) none
83. Corresponding to first quartile, the cumulative frequency is
(a) N /2 (b) N / 4 (c) 3N /4 (d) none
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84. Corresponding to second quartile, the cumulative frequency is
(a) N /4 (b) 2 N / 4 (c) 3N /4 (d) none
85. Corresponding to upper quartile, the cumulative frequency is
(a) 3N/4 (b) N / 4 (c) 2N /4 (d) none
86. The values which divide the total no. of observations into 10 equal parts are
(a) quartiles (b) percentiles (c) deciles (d) none
87. There are ————— deciles.
(a) 7 (b) 8 (c) 9 (d) 10
88. Corresponding to first decile, the cumulative frequency is
(a) N/10 (b) 2N /10 (c) 9N /10 (d) none
89. Fifth decile is equal to
(a) mode (b) median (c) mean (d) none
90. The values which divide the total no. of observations into 100 equal parts is
(a) percentiles ( b) quartiles (c) deciles (d) none
91. Corresponding to second decile, the cumulative frequency is
(a) N /10 (b) 2N /10 (c) 5N /10 (d) none
92. There are ———— percentiles.
(a) 100 (b) 98 (c) 97 (d) 99
93. 10th percentile is equal to
(a) 1st decile (b) 10th decile (c) 9th decile (d) none
94. 50th percentile is known as
(a) 50th decile (b) 50th quartile (c) mode (d) median
95. 20th percentile is equal to
(a) 19th decile (b) 20th decile (c) 2nd decile (d) none
96. (3rd quartile —— 1st quartile ) / 2 is
(a) skewness (b) median (c) quartile deviation (d ) none
97. 1st percentile is less than 2nd percentile.
(a) true (b) false (c) both (d) none
98. 25th percentile is equal to
(a) 1st quartile (b) 25thquartile (c) 24th quartile (d) none
99. 90th percentile is equal to
(a) 9th quartile (b) 90th decile (c) 9th decile (d) none
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100.1st decile is greater than 2nd decile
(a) True (b) false (c) both (d) none
101.Quartile deviation is a measure of dispersion.
(a) true (b) false (c) both (d) none
102.To define quartile deviation the
(a) lower & middle quartiles (b) lower & upper quartiles
(c) upper & middle quartiles (d) none are used.
102.Calculation of quartiles, deciles, percentiles may be obtained graphically from
(a) Frequency Polygon (b) Histogram (c) Ogive (d) none
103.7th decile is the abscissa of that point on the Ogive whose ordinate is
(a) 7N/10 (b) 8N /10 (c) 6N /10 (d) none
104.Rank of median is
(a) (n+ 1)/2 (b) ( n+ 1)/4 (c) 3(n + 1)/4 (d) none
105.Rank of 1st quartile is
(a) (n+ 1)/2 (b) ( n+ 1)/4 (c) 3(n + 1)/4 (d) none
106.Rank of 3rd quartile is
(a) 3(n+ 1)/4 (b) ( n+ 1)/4 (c) (n + 1)/2 (d) none
107.Rank of k th decile is
(a) (n+ 1)/2 (b) ( n+ 1)/4 (c) (n + 1)/10 (d) k( n +1)/10
108.Rank of k th percentile is
(a) (n+ 1)/100 (b) k( n+ 1)/10 (c) k(n + 1)/100 (d) none
109.—————— is equal to value corresponding to cumulative frequency (N + 1)/2 from
simple frequency distribution
(a) Median (b) 1st quartile (c) 3rd quartile (d) 4th quartile
110.———— is equal to the value corresponding to cumulative frequency (N + 1)/4 from
simple frequency distribution
(a) Median (b) 1st quartile (c) 3rd quartile (d) 1st decile
111.———— is equal to the value corresponding to cumulative frequency 3 (N + 1)/4 from
simple frequency distribution
(a) Median (b) 1st quartile (c) 3rd quartile (d) 1st decile
112.———— is equal to the value corresponding to cumulative frequency k (N + 1)/10 from
simple frequency distribution
(a) Median (b) kth decile (c) kth percentile (d) none
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113.———— is equal to the value corresponding to cumulative frequency k(N + 1)/100 from
simple frequency distribution
(a) kth decile (b) kth percentile (c) both (d) none
114.For grouped frequency distribution —————— is equal to the value corresponding to
cumulative frequency N /2
(a) median (b) 1st quartile (c) 3rd quartile (d) none
115.For grouped frequency distribution —————— is equal to the value corresponding to
cumulative frequency N /4
(a) median (b) 1st quartile (c) 3rd quartile (d) none
116.For grouped frequency distribution —————— is equal to the value corresponding to
cumulative frequency 3N /4
(a) median (b) 1st quartile (c) 3rd quartile (d) none
117.For grouped frequency distribution —————— is equal to the value corresponding to
cumulative frequency kN/10
(a) median (b) kth percentile (c) kth decile (d) none
118.For grouped frequency distribution —————— is equal to the value corresponding to
cumulative frequency kN /100
(a) kth quartile (b) kth percentile (c) kth decile (d) none
119.In Ogive, abscissa corresponding to ordinate N/2 is
(a) median (b) 1st quartile (c) 3rd quartile (d) none
120.In Ogive, abscissa corresponding to ordinate N/4 is
(a) median (b) 1st quartile (c) 3rd quartile (d) none
121.In Ogive, abscissa corresponding to ordinate 3N/4 is
(a) median (b) 3rd quartile (c) 1st quartile (d) none
122.In Ogive, abscissa corresponding to ordinate —————— is kth decile.
(a) kN/10 (b) kN/100 (c) kN/50 (d) none
123.In Ogive, abscissa corresponding to ordinate —————— is kth percentile.
(a) kN/10 (b) kN/100 (c) kN/50 (d) none
124.For 899 999 391 384 590 480 485 760 111 240
Rank of median is
(a) 2.75 (b) 5.5 (c) 8.25 (d) none
125.For 333 999 888 777 666 555 444
Rank of 1st quartile is
(a) 3 (b) 1 (c) 2 (d) 7
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126.For 333 999 888 777 1000 321 133
Rank of 3rd quartile is
(a) 7 (b) 4 (c) 5 (d) 6
127.Price per kg.( Rs.) : 45 50 35 Kgs.Purchased : 100 40 60 Total frequency is
(a) 300 (b) 100 (c) 150 (d) 200
128.The length of a rod is measured by a tape 10 times . You are to estimate
the length of the rod by averaging these 10 determinations.
What is the suitable form of average in this case——
(a) A.M (b) G.M (c) H.M (d) none
129.A person purchases 5 rupees worth of eggs from 10 different markets.You are to find the
average no. of eggs per rupee for all the markets taken together. What is the suitable
form of average in this case——
(a) A.M (b) G.M (c) H.M (d) none
130.You are given the population of India for the courses of 1981 & 1991. You are to find the
population of India at the middle of the period by averaging these population figures,
assuming a constant rate of increase of population.
What is the suitable form of average in this case—
(a) A.M (b) G.M (c) H.M (d) none
131.—————— is least affected by sampling fluctions.
(a) Standard deviation (b) Quartile deviation
(c) both (d) none
132.“Root –Mean Square Deviation from Mean“ is
(a) Standard deviation (b) Quartile deviation
(c) both (d) none
133.Standard Deviation is
(a) absolute measure (b) relative measure (c) both (d) none
134.Coefficient of variation is
(a) absolute measure (b) relative measure (c) both (d) none
135.—————— deviation is called Semi—interquartile range.
(a) Percentile (b) Standard (c) Quartile (d) none
136.———————— Deviation is defined as half the difference between the lower & upper
quartiles.
(a) Quartile (b) Standard (c)both (d) none
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137.Quartile Deviation for the data 1, 3, 4, 5, 6, 6, 10 is
(a) 3 (b) 1 (c) 6 (d)1.5
138.Coefficient of Quartile Deviation is
(a) (Quartile Deviation x 100)/Median (b) (Quartile Deviation x 100)/Mean
(c) (Quartile Deviation x 100) /Mode (d) none
139.Mean for the data 6,4,1,6,5,10,3 is
(a) 7 (b) 5 (c) 6 (d) none
140.Coefficient of variation = (Standard Deviation x 100 )/Mean
(a) true (b) false (c) both (d) none
141.If mean = 5, Standard deviation = 2.6 then the coefficient of variation is
(a) 49 (b) 51 (c) 50 (d) 52
142.If median = 5, Quartile deviation = 1. 5 then the coefficient of quartile deviation is
(a) 33 (b) 35 (c) 30 (d) 20
143.A.M of 2, 6, 4, 1, 8, 5, 2 is
(a) 4 (b) 3 (c) 4 (d) none
144.Most useful among all measures of dispersion is
(a) S.D (b) Q.D (c) Mean deviation (d) none
145.For the observations 6, 4, 1, 6, 5, 10, 4, 8 Range is
(a) 10 (b) 9 (c) 8 (d) none
146.A measure of central tendency tries to estimate the
(a) central value (b) lower value (c) upper value (d) none
147.Measures of central tendency are known as
(a) differences (b) averages (c) both (d) none
148.Mean is influenced by extreme values.
(a) true (b) false (c) both (d) none
149.Mean of 6, 7, 11, 8 is
(a) 11 (b) 6 (c) 7 (d) 8
150.The sum of differences between the actual values and the arithmetic mean is
(a) 2 (b) -1 (c) 0 (d) 1
151.When the algebraic sum of deviations from the arithmetic averages are not equal to zero,
the figure of arithmetic mean —————— correct.
(a) is (b) is not (c) both (d) none
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152.In the problem
No. of shirts : 30—32 33—35 36—38 39—41 42—44
No. of persons : 15 14 42 27 18
The assumed mean is
(a) 34 (b) 37 (c) 40 (d) 43
153.In the problem
Size of items : 1—3 3—8 8—15 15—26
Frequency : 5 10 16 15
The assumed mean is
(a) 20.5 (b) 2 (c) 11.5 (d) 5.5
154.The average of a series of over-lapping averages, each of which is based on a certain no. of
item within a series is known as
(a) moving average (b) weighted average
(c) simple average (d) none
155.————— averages is used for smoothening a time series.
(a) moving average (b) weighted average
(c) simple average (d) none
156.Pooled Mean is also called
(a) Mean (b) Geometric Mean (c) Grouped Mean (d) none
157.Half of the nos. in an ordered set have values less than the ——————— and half will
have values greater than the —————— .
(a) mean, median (b)median, median (c) mode ,mean (d) none.
158.The median of 27, 30, 26, 44, 42, 51, 37 is
(a) 30 (b) 42 (c) 44 (d) 37
159.For an even no. of values the median is the
(a) average of two middle values (b) middle value
(c) both (d) none
160.In the case of a continuous frequency distribution, the size of the —————— item
indicates class interval in which the median lies.
(a) (n-1)/2 th (b) (n+ 1)/2 th (c) n/2th (d) none
161.The deviations from median are ——————— if negative signs are ignored as compared
to other measures of central tendency.
(a) minimum (b) maximum (c) same (d) none
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162.Ninth Decile lies in the class interval of the
(a) n/9th (b) 9n/10th (c) 9n/20th (d) none item.
163.Ninety Ninth Percentile lies in the class interval of the
(a) 99n/100th (b) 99n/10th (c) 99n/200th (d) none item.
164.————— is the value of the variable at which the concentration of observation is the
densest.
(a) mean (b) median (c) mode (d) none
165.Height in cms : 60—62 63—65 66—68 69—71 72—74
No. of students : 15 118 142 127 18
Modal group is
(a) 66—68 (b) 69—71 (c) 63—65 (d) none
166.A distribution is said to be symmetrical when the frequency rises & falls from the highest
value in the ———————— proportion.
(a) unequal (b) equal (c) both (d) none
167.——————— always lies in between the arithmetic mean & mode.
(a) G.M (b) H.M (c) Median (d) none
168.Logarithm of G.M is the ——————— of the different values.
(a) weighted mean (b) simple mean (c) both (d) none
169.—————— is not much affected by fluctuations of sampling.
(a) A.M (b) G.M (c) H.M (d) none
170.The data 1,2,4,8,16 are in
(a) Arithmetic progression (b) Geometric progression
(c) Harmonic progression (d) none
171.————— & —————— can not be calculated if any observation is zero.
(a) G.M & A.M (b) H.M & A.M (c) H.M & G. M (d) None.
172.————— & ————— are called ratio averages.
(a) H.M & G.M (b) H. M & A.M (c) A.M & G.M (d) none
173.—————— is a good substitute to a weighted average.
(a) A.M (b) G.M (c) H.M (d) none
174.For ordering shoes of various sizes for resale, a —————— size will be more appropriate.
(a) median (b) modal (c) mean (d) none
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175.—————— is called a positional measure.
(a) mean ( b) mode (c) median (d) none
176.50% of actual values will be below & 50% of will be above —————
(a) mode (b) median (c) mean (d) none
177.Extreme values have ———— effect on mode.
(a) high (b) low (c) no (d) none
178.Extreme values have ———— effect on median.
(a) high (b) low (c) no (d) none
179.Extreme values have ———— effect on A.M.
(a) greatest (b) least (c) medium (d) none
180.Extreme values have ———— effect on H.M.
(a) least (b) greatest (c) medium (d) none
181.—————— is used when representation value is required & distribution is asymmetric.
(a) mode (b) mean (c) median (d) none
182.—————— is used when most frequently occurring value is required (discrete variables).
(a) mode (b) mean (c) median (d) none
183.—————— is used when rate of growth or decline required.
(a) mode (b) A.M (c) G.M (d) none
184.In ————, the distribution has open-end classes.
(a) median (b) mean (c) standard deviation (d) none
185.In ————, the distribution has wide range of variations.
(a) median (b) mode (c) mean (d) none
186.In ——— the quantities are in ratios.
(a) A.M (b) G.M (c) H.M (d) none
187.————— is used when variability has also to be calculated.
(a) A.M (b) G.M (c) H.M (d) none
188.————— is used when the sum of deviations from the average should be least.
(a) Mean (b) Mode (c) Median (d) None
189.————— is used when sampling variability should be least.
(a) Mode (b) Median (c) Mean (d) none
190.————— is used when distribution pattern has to be studied at varying levels.
(a) A.M (b) Median (c) G.M (d) none
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191.The average discovers
(a) uniformity in variability (b) variability in uniformity of distribution
(c) both (d) none
192.The average has relevance for
(a) homogeneous population (b) heterogeneous population
(c) both (d) none
193.The correction factor is applied in
(a) inclusive type of distribution (b) exclusive type of distribution
(c) both (d) none
194.“Mean has the least sampling variability“ prove the mathematical property of mean
(a) True (b) false (c) both (d) none
195.“The sum of deviations from the mean is zero“ —— prove the mathematical property of
mean
(a) True (b) false (c) both (d) none
196.“The mean of the two samples can be combined” — prove the mathematical property of
mean
(a) True (b) false (c) both (d) none
197.“Choices of assumed mean does not affect the actual mean”— prove the mathematical
property of mean
(a) True (b) false (c) both (d) none
198.“In a moderately asymmetric distribution mean can be found out from the given values of
median & mode“— prove the mathematical property of mean
(a) True (b) false (c) both (d) none
199.The mean wages of two companies are equal. It signifies that the workers of both the
companies are equally well-off.
(a) True (b) false (c) both (d) none
200.The mean actual wage in factory A is Rs.6000 whereas in factory B it is Rs.5500. It signifies
that factory A pays more to all its workers than factory B.
(a) True (b) false (c) both (d) none
201.Mean of 0, 3, 5, 6, 7, 9, 12, 0, 2 is
(a) 4.9 (b) 5.7 (c) 5.6 (d) none
202.Median of 15, 12, 6, 13, 12, 15, 8, 9 is
(a) 13 (b) 8 (c) 12 (d) 9
203.Median of 0.3, 5, 6, 7, 9, 12, 0, 2 is
(a) 7 (b) 6 (c) 3 (d) 5
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204.Mode of 0,3,5,6,7,9,12,0,2 is
(a) 6 (b) 0 (c) 3 (d) 5
205.Mode 0f 15,12,5,13,12,15,8,8,9,9,10,15 is
(a)15 (b) 12 (c) 8 (d) 9
206.Median of 40,50,30,20,25,35,30,30,20,30 is
(a) 25 (b) 30 (c) 35 (d) none
207.Mode of 40,50,30,20,25,35,30,30,20,30 is
(a) 25 (b) 30 (c) 35 (d) none
208.—————— in particular helps in finding out the variability of the data.
(a) Dispersion (b) Median (c) Mode (d) None
209.Measures of central tendency are called averages of the ———order.
(a) 1st (b) 2nd (c) 3rd (d) none
210.Measures of dispersion are called averages of the ———order.
(a) 1st (b) 2nd (c) 3rd (d) none
211.In measuring dispersion, it is necessary to know the amount of ———— & the degree of
—————.
(a) variation, variation (b) variation, median
(c) median, variation (d) none
212.The amount of variation is designated as —————— measure of dispersion.
(a) relative (b) absolute (c) both (d) none
213.The degree of variation is designated as —————— measure of dispersion.
(a) relative (b) absolute (c) both (d) none
214.For purposes of comparison between two or more series with varying size or no. of items,
varying central values or units of calculation, only —————— measures can be used.
(a) absolute (b) relative (c) both (d) none
215.The relation Relative range = Absolute range/Sum of the two extremes. is
(a) True (b) false (c) both (d) none
216.The relation Absolute range = Relative range/Sum of the two extremes is
(a) True (b) false (c) both (d) none
217.In quality control ———— is used as a substitute for standard deviation.
(a) mean deviation (b) median (c) range (d) none
218.—————— factor helps to know the value of standard deviation.
(a) Correction (b) Range (c) both (d) none
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219.———————— is extremely sensitive to the size of the sample
(a) Range (b) Mean (c) Median (d) Mode
220.As the sample size increases, —————— also tends to increase.
(a) Range (b) Mean (c) Median (d) Mode
221.As the sample size increases, range also tends to increase though not proportionately.
(a) true (b) false (c) both (d) none.
222.As the sample size increases, range also tends to
(a) decrease (b) increase (c) same (d) none
223.The dependence of range on extreme items can be avoided by adopting
(a) standard deviation (b) mean deviation (c) quartile deviation (d) none
224.Quartile deviation is called
(a) inter quartile range (b) quartile range (c) both (d) none
225.When 1st quartile = 20, 3rd quartile = 30, the value of quartile deviation is
(a) 7 (b) 4 (c) -5 (d) 5
226.(Q — Q )/(Q + Q ) is
3 1 3 1
(a) coefficient of Quartile Deviation (b) coefficient of Mean Deviation
(c) coefficient of Standard deviation (d) none
227.Standard deviation is denoted by
(a) square of sigma (b) sigma (c) square root of sigma (d) none
228.The mean of standard deviation is known as
(a) variance (b) standard deviation
(c) mean deviation (d) none
229.Mean of 25, 32, 43, 53, 62, 59, 48, 31, 24, 33 is
(a) 44 (b) 43 (c) 42 (d) 41
230.For the following frequency distribution
Class interval : 10—20 20—30 30—40 40—50 50—60 60—70
Frequency : 20 9 31 18 10 9
assumed mean is
(a) 55 (b) 45 (c) 35 (d) none
231.The value of the standard deviation does not depend upon the choice of the origin.
(a) True (b) false (c) both (d) none
232.Coefficient of standard deviation is
(a) S.D/Median (b) S.D/Mean (c) S.D/Mode (d) none
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233.The value of the standard deviation will change if any one of the observations is changed.
(a). True (b) false (c) both (d) none
234.When all the values are equal then variance & standard deviation would be
(a) 2 (b) -1 (c) 1 (d) 0
235.For values lie close to the mean, the standard deviations are
(a) big (b) small (c) moderate (d) none
236.If the same amount is added to or subtracted from all the values, variance & standard
deviation shall
(a) changed (b) unchanged (c) both (d) none
237.If the same amount is added to or subtracted from all the values, the mean shall increase
or decrease by the ———— amount
(a) big (b) small (c) same (d) none
238.If all the values are multiplied by the same quantity, the ————— & ———— also
would be multiple of the same quantity.
(a) mean, deviations (b) mean , median
(c) mean, mode (d) median , deviations
239.For a moderately non-symmetrical distribution, Mean deviation = 4/5 of standard deviation
(a) True (b) false (c) both (d) none
240.For a moderately non-symmetrical distribution, Quartile deviation = Standard deviation/3
(a) True (b) false (c) both (d) none
241.For a moderately non-symmetrical distribution, Probable error of standard deviation =
Standard deviation/3
(a) True (b) false (c) both (d) none
242.Quartile deviation = Probable error of Standard deviation.
(a) True (b) false (c) both (d) none
243.Coefficient of Mean Deviation is
(a) Mean deviation x 100/Mean or mode (b) Standard deviation x 100/Mean or median
(c) Mean deviation x 100/Mean or median (d) none
244.Coefficient of Quartile Deviation = Quartile Deviation x 100/Median
(a) True (b) false (c) both (d) none
245.Karl Pearson’s measure gives
(a) coefficient of Mean Variation (b) coefficient of Standard deviation
(c) coefficient of variation (d) none
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246.In ——— range has the greatest use.
(a) Time series (b) quality control (c) both (d) none
247.Mean is an absolute measure & standard deviation is based upon it. Therefore standard
deviation is a relative measure.
(a) True (b) false (c) both (d) none
248.Semi—quartile range is one-fourth of the range in a normal symmetrical distribution.
(a) Yes (b) No (c) both (d) none
249.Whole frequency table is needed for the calculation of
(a) range (b) variance (c) both (d) none
250.Relative measures of dispersion make deviations in similar units comparable.
(a) True (b) false (c) both (d) none
251.Quartile deviation is based on the
(a) highest 50% (b) lowest 25%
(c) highest 25% (d) middle 50% of the item.
252.S.D is less than Mean deviation
(a) True (b) false (c) both (d) none
253.Coefficient of variation is independent of the unit of measurement.
(a) True (b) false (c) both (d) none
254.Coefficient of variation is a relative measure of
(a) mean (b) deviation (c) range (d) dispersion.
255.Coefficient of variation is equal to
(a) Standard deviation x 100 / median (b) Standard deviation x 100 / mode
(c) Standard deviation x 100 / mean (d) none
256.Coefficient of Quartile Deviation is equal to
(a) Quartile deviation x 100 / median (b) Quartile deviation x 100 / mean
(c) Quartile deviation x 100 / mode (d) none
257.If each item is reduced by 15 A.M is
(a) reduced by 15 (b) increased by 15 (c) reduced by 10 (d) none
258.If each item is reduced by 10, the range is
(a) increased by 10 (b) decreased by 10 (c) unchanged (d) none
259.If each item is reduced by 20, the standard deviation
(a) increased (b) decreased (c) unchanged (d) none
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260.If the variables are increased or decreased by the same amount the standard deviation is
(a) decreased (b) increased (c) unchanged (d) none
261.If the variables are increased or decreased by the same proportion, the standard deviation
changes by
(a) same proportion (b) different proportion (c) both (d) none
262.The mean of the 1st n natural no. is
(a) n/2 (b) ( n-1)/2 (c) ( n+1)/2 (d) none
263.If the class interval is open-end then it is difficult to find
(a) frequency (b) A.M (c) both (d) none
264.Which one is true—
(a) A.M = assumed mean + arithmetic mean of deviations of terms
(b) G.M = assumed mean + arithmetic mean of deviations of terms
(c) Both (d) none
265.If the A.M of any distribution be 25 & one term is 18. Then the deviation of 18 from A.M
is
(a) 7 (b) -7 (c) 43 (d) none
266.For finding A.M in Step—deviation method, the class intervals should be of
(a) equal lengths (b) unequal lengths (c) maximum lengths (d) none
267.The sum of the squares of the deviations of the variable is —————— when taken about
A.M
(a) maximum (b) zero (c) minimum (d) none
268.The A.M of 1, 3, 5, 6, x, 10 is 6 . The value of x is
(a) 10 (b) 11 (c) 12 (d) none
269.The G.M of 2 & 8 is
(a) 2 (b) 4 (c) 8 (d) none
270.(n+1)/2 th term is median if n is
(a) odd (b) even (c) both (d) none
271.For the values of a variable 5, 2, 8, 3, 7, 4, the median is
(a) 4 (b) 4.5 (c) 5 (d) none
272.The abscissa of the maximum frequency in the frequency curve is the
(a) mean (b) median (c) mode (d) none
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273.variable : 2 3 4 5 6 7
no. of men : 5 6 8 13 7 4
Mode is
(a) 6 (b) 4 (c) 5 (d) none
274.The class having maximum frequency is called
(a) modal class (b) median class (c) mean class (d) none
275.For determination of mode, the class intervals should be
(a) overlapping (b) maximum (c) minimum (d) none
276.First Quartile lies in the class interval of the
(a) n/2th item (b) n/4th item (c) 3n/4th item (d) n/10th item
277.The value of a variate that occur most often is called
(a) median (b) mean (c) mode (d) none
278.For the values of a variable 3, 1, 5, 2, 6, 8, 4 the median is
(a) 3 (b) 5 (c) 4 (d) none
279.If y = 5 x - 20 & x bar = 30 then the value of y bar is
(a) 130 (b) 140 (c) 30 (d) none
280.If y = 3 x - 100 and x bar = 50 then the value of y bar is
(a) 60 (b) 30 (c) 100 (d) 50
281.The median of the nos. 11, 10, 12, 13, 9 is
(a) 12.5 (b) 12 (c) 10.5 (d) 11
282.The mode of the nos. 7, 7, 7, 9, 10, 11, 11, 11, 12 is
(a) 11 (b) 12 (c) 7 (d) 7 & 11
283.In a symmetrical distribution when the 3rd quartile plus 1st quartile is halved, the value
would give
(a) mean (b) mode (c) median (d) none
284.In Zoology, —————— is used.
(a) median (b) mean (c) mode (d) none
285.For calculation of Speed & Velocity
(a) G.M (b) A.M (c) H.M (d) none is used.
286.The S.D is always taken from
(a) median (b) mode (c) mean (d) none
287.Coefficient of Standard deviation is equal to
(a) S.D/A.M (b) A.M/S.D (c) S.D/GM (d) none
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(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:2)(cid:4)(cid:7)(cid:8)(cid:9)(cid:7)(cid:10)(cid:2)(cid:11)(cid:12)(cid:6)(cid:3)(cid:13)(cid:7)(cid:12)(cid:2)(cid:11)(cid:14)(cid:2)(cid:11)(cid:10)(cid:15)(cid:7)(cid:3)(cid:11)(cid:14)(cid:7)(cid:14)(cid:16)(cid:4)(cid:17)(cid:2)(cid:6)(cid:4)(cid:16)(cid:8)(cid:11)
288.The distribution , for which the coefficient of variation is less, is ——— consistent.
(a) less (b) more (c) moderate (d) none
AAAAANNNNNSSSSSWWWWWEEEEERRRRRSSSSS
1 (b) 2 (a) 3 (c) 4 (a) 5 (b)
6 (a) 7 (d) 8 (c) 9 (b) 10 (a)
11 (a) 12 (a) 13 (b) 14 (d) 15 (a)
16 (d) 17 (b) 18 (a) 19 (b) 20 (a)
21 (b) 22 (d) 23 (a) 24 (c) 25 (b)
26 (a) 27 (a)
31 (c) 32 (a) 33 (b) 34 (c) 35 (a)
36 (a) 37 (a) 38 (a) 39 (a) 40 (a)
41 (c) 42 (a) 43 (a) 44 (b) 45 (a)
46 (b) 47 (a) 48 (a) 49 (b) 50 (a)
51 (a) 52 (d) 53 (b) 54 (a) 55 (b)
56 (c) 57 (a) 61 (b) 62 (d) 63 (a)
64 (b) 65 (b) 66 (c) 67 (c) 68 (a)
69 (a) 70 (c) 71 (c) 72 (c) 73 (a)
74 (a) 75 (d) 76 (a) 77 (b) 78 (b)
79 (a) 80 (c) 81 (b) 82 (a) 83 (b)
84 (b) 85 (a) 86 (c) 87 (c) 91 (b)
92 (d) 93 (a) 94 (d) 95 (c) 96 (c)
97 (a) 98 (a) 99 (c) 100 (b) 101 (a)
102 (b) 103 (c) 104 (a) 105 (b) 106 (a)
107 (d) 108 (c) 109 (a) 110 (b) 111 (c)
112 (b) 113 (b) 114 (a) 115 (b) 116 (c)
117 (c) 121 (a)
122 (a) 123 (b) 124 (b) 125 (c) 126 (d)
127 (d) 128 (a) 129 (c) 130 (b) 131 (a)
132 (a) 133 (a) 134 (b) 135 (c) 136 (a)
137 (d) 138 (a) 139 (b) 140 (a) 141 (d)
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142 (c) 143 (c) 144 (a) 145 (b) 146 (a)
147 (b) 151 (b)
152 (b) 153 (c) 154 (a) 155 (a) 156 (c)
157 (b) 158 (d) 159 (a) 160 (c) 161 (a)
162 (b) 163 (a) 164 (c) 165 (a) 166 (b)
167 (c) 168 (a) 169 (b) 170 (b) 171 (c)
172 (a) 173 (c) 174 (b) 175 (c) 176 (b)
177 (c) 181 (c)
182 (a) 183 (c) 184 (a) 185 (a) 186 (b)
187 (a) 188 (c) 189 (c) 190 (b) 191 (a)
192 (b) 193 (b) 194 (b) 195 (a) 196 (a)
197 (a) 198 (b) 199 (b) 200 (b) 201 (a)
202 (c) 203 (d) 204 (b) 205 (a) 206 (b)
207 (b) 211 (a)
212 (b) 213 (a) 214 (b) 215 (a) 216 (b)
217 (c) 218 (a) 219 (a) 220 (a) 221 (a)
222 (b) 223 (c) 224 (a) 225 (d) 226 (a)
227 (b) 228 (a) 229 (d) 230 (c) 231 (a)
232 (b) 233 (a) 234 (d) 235 (b) 236 (b)
237 (c) 241 (b)
242 (a) 243 (c) 244 (a) 245 (c) 246 (b)
247 (b) 248 (a) 249 (c) 250 (b) 251 (d)
252 (b) 253 (a) 254 (d) 255 (c) 256 (a)
257 (a) 258 (c) 259 (c) 260 (c) 261 (a)
262 (c) 263 (b) 264 (a) 265 (b) 266 (a)
267 (c) 271 (b)
272 (c) 273 (c) 274 (a) 275 (a) 276 (b)
277 (c) 278 (c) 279 (a) 280 (d) 281 (d)
282 (d) 283 (c) 284 (c) 285 (c) 286 (c)
287 (a) 288 (b)
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