DISPERSION
1) The word dispersion is used to denote the ___ in the data.
A) degree of similarity
B) degree of homgineity
C) degree of heterogeneity
D) none of the above
2) All the directions are equal, the dispersion would be
A) - 1 B) 1 C) 0
D) data insufficient.
3) The wider the___from one observation to another, the larger will be the dispersion.
A) dispersion. B) similarity
C) jump. D) none
4) Quartile Deviation is also known as
A) Quartile range
B) interquartile range
C) semi interquartile range
D) mean deviation
5) Mean deviation is also known as
A) median deviation
B) median absolute deviation
C) absolute deviation
D) mean absolute Deviation.
6) All the____ measures of dispersion are defined as the ratio of an absolute measure of dispersion to the corresponding measure of Central tendency, and the ratio is expressed as a percentage.
A) absolute
B) relative
C) perfect D) none
7) which of the following is not CORRECT related to absolute and relative measure of dispersion ?
A) Absolute measures are expressed in the same unit in which the observations are given Relative measures are obtained by expressing an absolute measure as percentage of a measure of Central tendency, and hence relative measures are independent of the units of measurement.
B) Relative measures may also be used to compare the relative accuracy of data. But absolute measures cannot be so used.
C) Usually the absolute measures are employed for measuring dispersion. But for purposes of comparing the dispersion in different series, relative measures are used.
D) none of the above is not CORRECT. all are TRUE.
8) When we compare two or more distributions, we consider:
A) relative measures of dispersion.
B) absolute measures of dispersion.
C) neither A nor B
D) either A or B
9) which measure of dispersion is based on only the central 50% of the observations.
A) range
B) quartile deviation
C) standard deviation
D) mean deviation
10) Which measure of dispersion is based on all the observations?
A) standard deviation
B) quartile deviation
C) mean deviation
D) both A and C above
11) Which measures of dispersion represents the maximum possible difference between any two observations.
A) standard deviation
B) mean deviation
C) range
D) quartile deviation
12) quartile deviation is
A) difference between the upper and the lower quartiles.
B) sum of upper and the lower percentile.
C) half the difference between the upper and the lower quartiles
D) none of the above.
13) The unpopularity of quartile deviations lies in the fact that it:
A) takes into account all the observations.
B) does not depend on the magnitudes of all observations.
C) can be calculated with open end class intervals.
D) inferior to range as a method of absolute measure of dispersion.
14) For a open-end classes in the frequency distribution, which of the following measures dispersion can be calculated?
A) range
B) standard deviation
C) mean deviation
D) quartile deviation
15) mean deviation has the minimum value when taken from:
A) Arithmetic mean
B) Geometric mean
C) median
D) mode
16) Standard deviation is also known as
A) root mean deviation
B) root mean square deviation
C) root square deviation
D) mean square deviation
17) The square of standard deviation is a known as
A) deviation
B) variation
C) variance
D) covariance
18) standard deviation is:
A) negative square root of a variance.
B) positive square root of variance
C) either A or B
D) both A and B
19) All measures of dispersion are dependent on change of____ but are change of___
A) scale, origin. B) origin, scale
C) Time, Scale D) none
20) The standard deviation of two values a and a b is equals to
A) sum of the two values
B) half their difference
C) their difference
D) square root of their difference.
21) Mean deviation about an arbitrary origin A is defined as:
A) half difference between the upper and lower quartiles.
B) the mean of absolute deviation from A
C) The difference between the largest and the smallest atems.
22) standard deviation of a given set of observations is defined as
A) the mean of absolute deviations from the mean of the distribution.
B) the root square deviation from mean.
C) the root mean square deviation from median.
D) the root mean square deviation from mean
23) Coefficient of Variation is defined as:
A) the ratio of standard deviation to median.
B) the ratio of standard deviation to Arithmetic mean .
C) the ratio of standard deviation to Arithmetic mean multiplied by hundred.
D) none of the above.
24) which of the following measures of dispersion has some Mathematical properties?
A) quartile deviation
B) mean deviation
C) standard deviation
D) range .
25) which of the following measure of dispersion would you use to use to find a pooled measure of dispersion after combining several groups ?
A) mean deviation about median
B) quartile deviation
C) mean deviation about mode
D) standard deviation
26) Coefficient of quartile deviation is defined as:
A) the ratio of quartile deviation to mode, multiplied by 100.
B) the ratio of QD to median
C) the ratio of QD to median, multiplied by 100
D) the ratio of QD to range multiplied by 100.
27) Root mean square deviation is minimum when deviations are taken about____
A) Arithmetic mean
B) median
C) mode
D) harmonic mean.
28) standard deviation is __ when all the observations are equal
A) 1 B) 0. C) -1.
D) can't be determined.
29) Standard deviation of one observation observation is__
A) 1 B) 2 C) 0
D) can't be determined
30) The quickest measure of dispersion is____
A) standard deviation
B) mean deviation about mean
C) range
D) interquartile range
31) The appropriate measure of dispersion from a frequency distribution with open-end class is____
A) mean deviation
B) quartile deviation
C) standard deviation
D) range
32) The most useful measure of dispersion is:
A) range
B) Quartile deviation.
C) mean deviation
D) standard deviation
33) For comparing the variability of two or more distribution whose means differ widely, appropriate measure of dispersion is:
A) coefficient of range
B) Coefficient of variation
C) coefficient of quartile deviation
D) none of the above
34) For any two numbers, standard deviation is:
A) square of their range
B) double of the range
C) half of the range
D) thrice the range
35) Which of the following statement is true ?
A) mean is is absolute measure and standard deviation is based upon it. therefore , standard deviation is a relative measure.
B) For a symmetrical distribution, semi interquartile range is 1/4 of the range.
C) whole frequency table is needed for the calculation of quartile deviation.
D) none of the above.
36) following are the wages of 8 workers expressed in Rs. 82, 96, 52, 75, 65, 70, 70, 50. find the range and also its coefficient
A) Rs 42, 31.51%
B) Rs46, 31.51%
C) Rs46, 31.15%
D) Rs46, 30.15%.
37) If the relationship between x and y is given 2x+ 3y=10 and the range of x is Rs9, what would be the range of y ?
A) Rs 10 B) Rs6 C) Rs9.5 D) N
38) If x and y are related as 4x+ 3y+11= 0 and mean deviation of x is 4.80, what is the mean deviation of y?
A) 3.60. B) 6.40. C) 4.60. D) 7.20
39) The standard deviation calculated from a set of 32 observations is 5. If the sum of the observations is 80, what is the sum of the squares of these observations?
A) 10. B) 1000. C) 100. D) 2000
40) If Arithmetic mean and coefficient of variation of x are 10 and 40 respectively, what is the variation of if the quartile variance of (5-x) ?
A) 9 B) 16 C) 25. D) 64
41) If the quartile deviation of x is 3 and 3x+6y= 20, What is quartile Deviation of y ?
A) 3 B) 3.5 C) 2 D) 1.5
42) The mean and standard deviation calculated from 20 observations are 15 and 10 respectively. If an additional observation 5, left out through oversight, be included the calculation, find the correct mean and standard deviation.
A) 14.52, 9.99. B) 14, 10
C) 14.52, 9. D) 14, 9.99
43) The mean income per month of a friendly Society of 25 members is Rs.350 and the standard deviation is Rs. 50. five more members are admitted to the society and their incomes in Rs. Per month are 260, 300, 320, 490 and 590. Find the standard deviation of income for the new group of 30 members.
A) 70 B) 71 C) 70.65 D) 71.65
44) What is the standard deviation of the two values 10 and 7?
A) 17 B) 3. C) 1.5. D) none
45) standard deviation of two quantities is 3. if one of the number is 7, find the other.
A) 1. B) 13. C) either A or B. D) N
46) What is the standard deviation of six numbers: 7,7, 7,9, 9,9
A) 1 B) 2 C) 0 D) 0.5
47) for two values of a values x, the mean and the standard deviation are 10 and 2 respectively. what are the values of x.
A) 7, 13 B) 8,12 C) 10,10 D) N
48) When variance(x)= 0, what can you say about the set of observations?
A) all the values are low in magnitude.
B) all the values are very high in magnitude.
C) all the values are not equal.
D) all the values are equal.
49) Which of the following statement(s) it is TRUE ?
A) when all observations are same, any measure of dispersion would be 1.0.
B) mean absolute deviation from median and mean are 5 and 3 respectively.
C) the unit of a variance is that of the observations.
D) none of the above is true.
50) If the third quartile is 30 and median 22, find the coefficient of quartile deviation, assuming the distribution to be asymmetrical.
A) 36. B) 35.4. C) 36.4. D) 37.8
51) find the range and relative range of the daily wages (in Rs.) of 10 persons: 24, 18, 25, 16, 20, 28, 22, 17, 21, 27.
A) Rs.11 B) 12 C) 13 D) 14
52) Find out the range of the following data :
Height Number of students.
60-62 8
63-65 27
66-68 42
69-71 18
72-74 5
A) 14 B) 15 C) 14.5 D) 15.5
53) find the mean deviation about median for the following data 8, 15, 53, 49, 19, 62, 7, 15, 95, 77.
A) 26 B) 27 C) 27.2 D) 27.8
54) The marks obtained by 10 students in an examination where as follows: 70, 65, 68, 70, 75, 73, 80, 70, 83, 86,. find the mode, median and mean deviation about mean.
A) 70, 71.5, 5.6
B) 71.5, 70, 6.5
C) 70, 71.5, 6.5
D) 70, 75.1, 5.6
55) Find the mean deviation about mean of the first 10 natural numbers.
A) 3. B) 4. C) 3.5. D) 2.5
56) For a set of ungrouped values the following sums are found: N= 15, ∑x= 480, ∑x²=15735, find the mean and standard deviations of the values.
A) 30.3 B) 31.5 C) 32.5 D) 32.3
57) find the standard deviation of the series: 1, 2,3, 4, t, 6, 7, 8, 9, 10, 11
A) 3 B) 2.16 C) 3.96 D) 3.16
58) The variance of first n positive integers is:
A) (n²-1)/12. B) (n²-1)/6
C) (n²+1)/12. D) none
59) the standard deviation of 1, 2, 3,......n is√14; find n.
A) 11. B) 12. C) 13. D) 14
60) a sample of size 15 has a mean 3.5 and the standard deviation 3.0. another sample of side 22 as a mean 4.7 and standard deviation 4.0. if the two samples are pooled together, find the standard deviation of the combined sample.
A) 2.68. B) 4. C) 3.68. D) 3.5
61) the mean and standard deviation of a sample size 10 were found to be 9.5 and 2.5 respectively. later on an additional of the observation became available. this was 15.0 and was included in the original sample. find the mean and standard deviation of the 11 observations.
A) 10,2.86 B)9.86, 2 c) 10, 2 d) N
62) For a group containing 100 observations, the group containing the Arithmetic mean and standard deviation were 8 and √10.5. for 50 observations selected from these 100 observations the mean of the standard deviation are 10 and 2 respectively. find the Arithmetic mean and standard deviation of the other half.
A) 3,3 B) 6,3 C) 6,4 D) 5,3
63) the first two sample has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation √13.44, find the S. D of the second group.
A) 2. B) 3. C) 4. D) 1
64) A student obtained the mean and the standard of 100 observations as 40 and 5.1 respectively. it was later found that he had wrongly copied one observation as 50, the correct figure being 40. calculate the correct mean the correct SD.
A) 40, 5. B) 39.9, 5
C) 40, 4.8. D) 39.9, 4.98
65) the mean and the standard deviation of 20 items is found to be 10 and 2 respectively. at the time of checking, it was found that one items 8 was incorrect. calculate the mean and standard deviation. if the wrong item is omitted.
A) 10.1053, 1. B) 10.1053, 1.997
C) 11, 1.9. . D) none
66) taking data from the previous question, calculate mean and standard deviation if wrong item is replaced by 12.
A) 10, 1.99. B) 10, 2
C) 10.2, 1.99. D) none
67) in a distribution of 200 boys, where 0-5, 5-19, are groups, mean and standard deviation are 40 and 15 respectively. on checking it was found that the marks obtained by one student was wrongly student was wrongly entered as 53 instead of 43. find the correct mean , SD
A) 39, 15. B) 36, 14
C) 39.95, 14.97. D) 36.65, 15.97
68) weekly wages of workers in a factory increases from Rs.8 to Rs12 and standard deviation increases from Rs.1 to Rs. 5 . have the wages become less uniform now ?
A) no. B) yes
C) can't say D) no change
69) calculate the mean deviation about Arithmetic mean from the following:
X. F
5 8
15 12
25 10
35 8
45 3
55 2
65 7
A) 0.55. B) 0.75. C) 7.5. D) none
70) The mean deviation about the mean for the following data is:
Daily wages number of workers
8-11 5
12-15 11
16-19 20
20-23 10
24-27 4
A) 3. . B) 1.21. C) 4 D) 4.56
71) find the quartile deviation of the following distribution:
Height. Number of students
60 4
62 10
64 18
66 26
68 20
70 12
72 5
A) 1.5. B) 2.5. C) 2. D) 3
72) The quartiledeviation of the following distribution is :
weight number of men
40-45 10
4-45 22
50-55 28
55-60 20
60-65 12
65-70 8
A) 4. B) 5. C) 5.17. D) 4.71
73) The standard deviation of the following data is :
Weight number of men
50. 30
55 40
60 65
65 50
70. 15
A) 5.49 B) 5.59 C) 5.79. D) 6.19
74) The standard deviation of the the of the following distribution is
Turnover (Rs) No. Of Items
050-100 5
100-150 8
150-200. 9
200-250. 12
250-300. 18
300-350 23
350-400 17
A) 86480. B) 88480
C) 89480. D) 88800
75) what is the standard deviation of the following frequency distribution ?
Weight number of boys
120-124 12
115-129 25
130-134 28
135-139 15
140-144 12
145-149 8
A) 6.15. B) 6.18 C) 7.18 D) 8.81
76) from the following data, calculate the value of a mean and the standard deviation.
Age-group number of employee
Below 20 20
20-25 26
25-30 44
30-35. 60
35-40 101
40-45 109
45-50 84
50-55 56
55 and above 10
A) 39.25, 9.60. B) 40, 10
C) 39.845, 9.645 D) none
77) calculate the variance from the following data:
Age (years) frequency
10-19 3
20-29 61
30-39 50
40-49 32
50-59 20
60-69 4
A) 121 B) 192 C) 129 D) 138
78) when you mean =22.5, standard deviation = 2.5, then what is the value of coefficient of variation ?
A) 9.09% B) 11.11%
C) 12.25% D) 16.67%
79) find the coefficient of mean deviation for the following series:
487, 508, 620, 382, 408, 266, 186, 218.
A) 29.73% B) 30.13%
C) 30.73%. D) none
80) Find the coefficient of variation for the following series: 40, 30, 80, 60, 50, 90, 70
A) 32% B)30% C)33.33% D)36.67%
81) find the coefficient of variation of the following data.
marks. number of students
0-10 4
10-20 10
20-30 16
30-40 12
40-50 8
A) 40.89% B) 42.19%
C) 52.13%. C) 43.19%
82) what is the coefficient of variation of the following distribution
weight(in gms). frequency
110-119 5
120-129 7
130-139 12
140-149 20
150-159 16
160-169 10
170-179 7
180-189 3
A) 10.25% B) 11.75%
C) 12.25% D) 11.69%
83) Mean and variance of two series is series is given below. which series is more stable?
A: mean = 53; variance= 7
B: mean= 105 ; variance= 4
A) series B. B) series A
C) both are equally stable
D) none of the above
84) from the data given below, state which series is more consistent:
Variable. series A. series B
10-20 10. 18
20-30 18 22
30-40 32 40
40-50. 40 32
50-60 22 18
60-70 18 10
A) Series A. B) Series B
C) both are equally consistent
D) nothing can be said
85) prices of a particular commodity in 5 years in two cities are given below. find from the data the city which had more stable prices:
prices in city A. prices in city B
20 10
22 20
19 18
23 12
26 15
A) city B.
B) both the cities has equally stable prices.
C) city A
D) cannot be determined
86)
87) If each item is reduced by 5. the range is:
A) increased by 5
B) decreased by 5
C) remains unchanged
D) none of the above
88) if each item is reduced by 2², the standard deviation is:
A) increased
B) decreased
C) neither A nor B
D) either A or B
89) If all the variables are increased or decreased by the same amount the standard deviation:
A) decreases or increases respectively.
B) increases or decreases respectively
C) remains unchanged
D) can't be determined.
90) the distribution, for which the coefficient of variation is less, is____ consistent.
A) less. B) moderate
C) more D) none of the above
91) In a frequency distribution, the three quartiles are 25, 50 and 75. What is the value of quartile deviation deviation and its coefficient ?
A) 25, 0.667 B) 25, 0.533
C) 25, 00.50 D) 25, 0.475
92) calculate the mean deviation about the mean for the following data and find its coefficient: 10, 12, 14, 15, 15, 13, 15, 10, 12, 14
A) 1.45, 0.1231. B) 1.6, 0.1231
C) 1.4, 0.1231. D) 1.6, 1.231
93) calculate the standard deviation for the following data: 74, 47, 90, 37, 84, 51, 40, 66, 54, 59,
A) 16. B)16.98 C) 17.10. D) 15.75
94) taking data from previous question, what would be the coefficient of variation for the data given;
A) 27% B) 28%. C) 29% D) 28.4%
# Read the following data then answer the questions asked.
the following data related to the salary of workers of two factories
FactoryA Factory B
No.of workers: 80 110
Mean: Rs. 2320 Rs.2160
SD: Rs 120 Rs 122
95) In which factory is the total expenditure on salary more?
A) factory A. B) factory B
C) both the factories total expenditure is same
D) none of the above
96) In which factory is average salary of workers more ?
A)factory A. B) factory B
C) can't be determined
D) none of the above
97) In which factory is variance in salary more ?
A) factory A. B) factory B
C) both the factories are equally stable
D) none of the above
98) If standard deviation of u is 3, what is the variance of (15-2u) ?
A) 9. B) 36. C) 16. D) none
99) If the mean and standard deviation of"x" are a and b respectively, then the standard deviation of (x-a)/b is:
A) 1. B) ab. C) a+b. . D) -1
100) If the standard deviation of 1st n natural numbers is 4, then the value of n is:
A) 4. B) 6. C) 7. D) 9
ANSWERS
1. C. 11. C. 21. B. 22. D. 23. C
2. C. 12. C. 24. C. 25. D. 26. C
3. A. 13. B. 27. A. 28. B. 29. C
4. C. 14. D. 30. C. 31. B. 32. D
5. D. 15. C. 33. B. 34. C. 35. B
6. B. 16. B. 36. B. 37. B. 38. B
7. D. 17. C. 39. B 40. B. 41. D
8. A. 18. B. 42. A. 43. C. 44. C
9. B. 19. B. 45. C. 46. A. 47. B
10. D. 20. B. 48. D. 49. D. 50. C
51. B 52. B. 53. C. 54. A. 55. D
56. C. 57. D. 58. A. 59. C. 60. C
61. A 62. B. 63. C. 64. B. 65. B
66. C. 67. C. 68. B. 69. B. 70. B
71. C. 72. C 73. C. 74. B 75. C
76. A. 77. C. 78. B. 79. C. 80. C
81. D. 82. B. 83. A 84. B. 85. C
86. A. 87. C. 88. C. 89. C. 90. C
91. C. 92. B. 93. C. 94. D. 95. B
96. A. 97. B. 98. B 99. A 100. C
Exercise--2
____________
1) Calculate the standard deviation for the following natural number 1, 2, 3, 4 ,5,6,7. Compute also their mean deviation about mean. 2.1, 7.1
2) Determine the mean deviation about median for the following number 16, 19, 29, 36, 46, 55, 62, 69, 75, 88. 20.4
3) calculate the quartile deviation the coefficient of quartile deviation for the following:
X: 15 30 45 60 75 90
Y: 4 7 15 8 7 2 15, 0.33
4) The coefficient of variation for the two series are 58% and 69% respectively. Their standard deviations are 21.2 and 15.6. compute their A. M. 36.55, 22.6
5) Wages paid last year to the cleaning and maintenance staff of a shopping mall had a mean of ₹30000 with a standard deviation of ₹2400. what will be the new mean and standard deviation if all wages are increased by
A) 3000
B) 10 %.
If the cleaning and maintenance staff has been complaining of the disparity of wages paid to them, which of the policies (A) or (B) will take care of their complaint better ? 2400, 2640. (A)
6) the following facts were gathered regarding industrial dispute:
Information before after
No. Of workers 516 508
Mean wages 49.50 51.75
Median wages 52.70 50
Variance 100 121
Compare the position before and after the dispute in terms of modal wages and coefficient of variation.
7) ) Daily expenses % of household
000 - 199 18.9
200- 399 26.9
400- 599 30.8
600- 799 10.4
800- 999 9.0
1000 & above 4.0
Can you compute the standard deviations from the above data?
8) Expenditure No. Of families
< 1000 30
1000-1250 45
1250-1500 70
1500-1750 82
1750-2000 66
2000-2250 57
2250-2500 28
2500-2750 22
2750-3000 18
>3000 12
Can you compute the standard deviation from the above data?
9) the mean and standard deviation of height reading of a group of an employees of a firm are found to be 172cm and 18cm, while the same measures for the weight reading at 65kg and 9kg. Compare the variability of the height reading with the that of the weight readings. Former one
10) find the dispersion using suitable measure:
Farm size number of firms
00-40 394
41-80 461
81-120 391
121-160 334
161-200 169
201-240 113
241 and over 148
11) Find the mean deviation from mean of 10 equal samples values. 0
12) what is the range of the daily wages(in ₹) of 7 persons: 12, 7 15, 10, 19, 17, 25. 18
13) find the range for the following data on marks of a student in a class 9, 7, 25, 18, 38, 12, 30, 35. 31
14) Find the range for the following: 24 18,25 ,16,20, 28,22, 17,21,27. 12
15) what is the quartile deviation of: 12, 7, 15, 10, 19, 17, 25.
A) 2.5 B) 3.5 C) 4.5 D) 5.4
16) what is the quartile deviation/ semi inter-quartile range of the daily wages(in ₹) of 7 persons: 350, 840, 650,710, 980, 575, 290
A) 245 B) 345 C) 425 D) 524
17)find out the quartile deviation.
Height in inch No.of students
50-53 2
53-56 7
56-49 24
59-62 7
62-65 13
65-68 3
A) 2.72 B) 2.29 C) 2.92 D) 2.27
18) what is the mean deviation of median for the following data 8,15, 53, 49, 19, 62, 7, 15, 77, 95.
A) 22.2 B) 27.2 C) 29.2 D) 25.2
19) what is the mean deviation of median for the following data: 13, 84, 68, 24, 96, 139, 84, 27.
A) 22.28 B) 33.88 C) 29.23 D) 25.28
20) what is the mean deviation of median for the following data: 8, 15, 53, 49, 19, 62, 7, 15, 95, 77.
A) 22.2 B) 23.8 C) 27.2 D) 25.2
21) what is the mean deviation of mean for the following data: 31, 35, 29, 63, 55, 72, 37.
A) 14.82 B)16.28 C)19.26 D) 15.24
22) what is the mean deviation of mean for the following data sets: 27, 33, 49, 61, 76, 104, 126
A) 24.82 B) 27.28 C) 29.14 D) 25.24
23) what is the mean deviation of the mean for the following data 29, 35, 51, 63, 78, 106, 128
A) 24.82 B) 27.28 C) 29.26 D) 29.14
24) what is the mean deviation of mean for the following data: 31, 35 , 29, 63,55, 72, 37
A) 14.86 B) 17.28 C) 19.26 D) 15.24
25) what is the mean of the following data
X: 10 11 12 13 14 Tot
f: 3 12 18 12 3 48
A) 0.26 B) 0.24 C) 0.75 D) 0.82
26) what is the mean deviation of median for the following data:
X: 10 11 12 13 14 Total
F: 3 12 8 12 3 48
A) 0.75 B) 0.82 C) 0.24 D) 0.57
27) what is the mean deviation for the following data
X: 5 7 9 11 13 Total
F: 4 10 22 10 4 50
A) 1.42 B) 1.46 C) 1.44 D) 1.48
28) what is the mean deviation about mean for the following data set:
X: 5 10 15 20 total
F: 8 2 4 8 20
A) 6.40 B) 6.06 C) 6 D) 6.08
29) from the following data set, find the mean deviation about mean:
7, 9, 16, 24, 26, 31, 39.
A) 9.47 B) 9.41 C) 9.37 D) 9.24
30) from the following data set, find the mean deviation about median
7, 9, 16, 24, 26, 31, 39.
A) 9.14 B) 9.17 C) 9.24 D) 9.34
31) what is the mean deviation about mean from the first ten natural numbers?
A) 2.2 B) 2.4 C) 2.3 D) 2.5
32) the standard 1,2,3...., n is √14. What is the value of n.
A) 11 B) 13 C) 12 D) 14
33) what is the mean deviation of median for the following:
Class interval: 2-4 4-6 6-8 8-10
Frequency: 3 4 2 1
A) 1.70 B) 1.8 C) 1.4 D) 1.5
34) what is the mean deviation of median for the following set ?
C-I: 2-6 6-10 10-14 14-18
F: 6 8 4 2
A) 2. 7 B) 2.8 C) 2.4 D) 2.5
35) what is the standard deviation for the following: 1,2,3,4,5,6,7,8,9
A) 2.78 B) 1.58 C) 1.48 D) 2.58
36) what is the standard deviation for the following: 49, 63, 46, 59, 65, 52, 60, 54.
A)36.7 B)34.9 C)36.4 D)36.5
37) what is the standard deviation for the following: 20,85,120,60,40.
A)6.78 B)6.36 C)6.48 D)6.58
38) what is the standard deviation for: 4, 5, 6, 6, 7, 8
A) 1.78 B) 1.29 C) 1.48 D) 1.58
39) what is the standard deviation for: 3, 5,11,7,8,10,9, 12, 14, 11
A) 3.78 B)3.58 C)3.48 D)3.16
40) What is the standard deviation: 240.12, 240.13, 240.15, 240.12, 240.17, 240.15, 250.17, 240.16
A) 0.0785 B) 0.0585 C) 0.0325 D) 0.0352
41) what is the standard deviation of 1,2,3,4,5,6,7,8,9,10
A) 2.77 B)2.87 C)2.47 D) 2.57
42) what is the standard deviation of 1,2,3,4,5,6,7,8,9,10, 11
A) 3.76 B)3.16 C)3.46 D) 4.56
43) For a set of grouped values the following sums are found: N= 15, ∑x= 480, ∑x²= 15735. find the standard deviation.
A) 3 B) 5 C) 4 D) 6
44) calculate the variance of 1,5,6
A) 5.66 B) 4.86 C) 4.76 D) 4.96
45) what is the variance of the first n positive integers ?
A) (n²-1)/12 B)(n²-3)/12 C) 2(n²-1)/3 D) (n²-2)/12
46) what is the mean deviation about mean the following data:
Daily wages No.of workers
8-11 5
12-15 6
16-19 20
20-23 10
24-27 4
A) 3.12 B) 3 21 C) 3.25 D) 3.52
47) what is the standard deviation for the following data
Daily wages No.of workers
10 7
20 18
30 25
40 27
50 14
60 7
A) 13.12 B)13.56 C)13.25 D)13.52
48) what is the standard deviation for the following data.
Daily wages No.of workers
25 60
36 130
45 150
55 130
65 30
A)11.12 B)11.56 C)11.07 D)11.52
49) what is the standard deviation for:
Weight (x): 50 55 60 65 70
Men(f): 30 40 65 50 15
A)5.69 B)5.79 C)5.49 D)5.59
50) what is the standard deviation of the following data set giving the age distribution of 540 members of parliament ?
Age(x): 30 40 50 60 70
frequency(f): 64 132 153 140 51
A)11.78 B)11.64 C)11.48 D)11.58
51) what is the standard deviation for the following data set?
Height in inch No.of students
59-61 4
61-63 30
63-65 45
65-67 15
67-69 6
A) 1.58B)1.38 C)1.85 D)1.83
52) what is the standard deviation of the following:
Wages: 20-24 25-29 30-34 35-39
F:. 16 28 14 12
A) 5.5 B)5.08 C) 5.05 D) 5.04
53) what is the standard deviation for the following.
Weight No of students
120-124 12
125-129 25
130-134 28
135-139 15
140-144 12
145-149 8
A)7.58 B)7.38 C)7.18 D)7.81
54) the mean of two samples of size 50 and 100 respectively are 54.4 and 503; and their SDs are 8 and 7 respectively. what is the mean and SD of the combined set of observations?
A) 51.7 and 7.6 B) 51.7 and 7.8 C) 50.7 and 7.6 D) 50.7 and 7.8
55) A sample size 15 has mean 3.5 and standard deviation 3.0. Another sample of size 22 has mean 4.7 and standard deviations 4.0. if the two samples are pooled together, find the mean and standard deviation of the combined sample.
A) 4.21, 4.68 B) 3.21, 3.68 C) 4.21, 3.67 D) 3.21, 4.68
56) the mean and standard deviation of 20 items is found to be 10 and 2 respectively. At the time of checking, it was found that one item 8 was incorrect. calculate the SD if the wrong item is replaced by 12.
A) 1.909 B) 1.099 C) 1.990 D) 1.9
57) the mean and SD of a simple size 10 were found to be 9.5 and 2.5 respectively. Later on additional observation became available. this was 15 and it was included in the original sample. find SD of the 11 observations.
A) 2.68 B) 2.48 C)2.84 D) 2.86
58) For a group of containing 100 observations, the mean and SD are 8 and √10.5 for 50 observation selected from these 100 observations the mean and SD are 10 and 2 respectively. find the mean and SD of the other half:
A) 6,2 B) 5,4 C) 6,3 D) 5,5
59) the mean and SD of 20 items is to be 10 and 2 respectively. At the time of checking, it was found that one item 8 was incorrect. Calculate the SD if the wrong item is omitted.
A) 1.799 B) 1.997 C) 1.979 D) 1.907
60) the first two samples has 100 items with mean 15 and SD 3. If the whole group has to 250 items with mean 15.6 and SD √13.44, find the SD of the second group.
A) 3 B) 4 C) 5 C) 6
61) in a distribution of 200 boys, where 0-5 , 5-10 etc are groups, mean, SD are 40 and 15 respectively. On checking it was found that marks obtained by one student was wrongly entered as 53 in place of 43. find the corrected SD
A) 14.17 B)14.77 C)14.57 D)14.97
62) A student obtained the mean and SD of 100 observations as 40 and 5.1 respectively. It was later found that he had wrongly copied one observation as 50, the correct figure being 40. Calculate the correct mean and SD.
A) 39.9,5 B) 35.9,9 C)39.5,9 D)39.5,5
63) Find the coefficient of variation of the: 5, 10, 30, 40, 65
A)72.26 B)72.62 C)72.36 D)72.46
64) Find the coefficient of variation of: 40, 30, 80, 60, 50, 90, 70.
A)33.26 B)33.33 C)33.36 D)33.44
65) What is the SD of variation of:
Marks No of students
00-10 5
10-20 10
20-30 20
30-40 40
40-50 30
50-60 20
60-70 10
70-80 4
A)15.67 B)15.65 C)15.69 D) 15.63
66) What is the coefficient of variation of:
Marks No of students
01-10 5
11-20 12
21-30 20
31-40 25
41-50 40
51-60 22
61-70 15
71-80 6
81-90 4
91-100 1
Total 100
A)41.2 B)45.2 C)42.5 D) 52.4
67) What is coefficient of mean deviation about median for: 46, 79, 26, 85, 39, 65, 99, 29, 56, 72.
A)33.27 B)33.72 C)33.77 D)33.22
68) What is the coefficient of mean deviation for: 10,20,40,60,70,100.
A)53.27 B)53.34 C)53.77 D)53.22
69) What is the coefficient of mean deviation for: 487, 508, 620, 382, 408, 266, 186, 218.
A)30.27 B)30.73 C)30.77 D)30.22
70) Prices of a particular commodity in five years in two cities are given below:
Prices in city A. Prices in city B
20 10
22 20
19 18
23 12
26 15 Find the city which had more stable prices
A) A B) Both A and B C) B D) n
71) Which factory has greater variability in industry wages?
Factory Average SD Employees
A 34.5 5 476
B 28.5 4.5 524
A) A B) Both A and B C) B D) n
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