EXERCISE -1
1) The average discovers:
A) uniformity in variability
B) variability in uniformity
C) either A or B
D) both A and B
2) the correction factor is applied in:
A) inclusive type of distribution B) exclusive type of distribution C) both type of distribution D) none
3) which of the following statement is not correct ?
A) the sum of deviation from mean is zero
B) the mean of the two samples can be combined
C) mean has the least sampling variability.
D) choice of assumed mean does not affect the actual mean.
4) which of the following is the basic assumptions made while computing the arithmetic mean from a grouped frequency distribution ?
A) all the classes and equal weights
B) all class intervals are of same width.
C) all the values of a class are equal to the mid value of that class
D) all of the above.
5) median is better suited for___interval series.
A) positional B) continuous C) discrete D) none.
6) In case of odd number of observations which of the following describes median?
A) the simple average of the two middle values.
B) simply the middle value.
C) the weighted average of the two middle most values.
D) any of the two middle most value
7) In case of even number of observations which of the following best describes median?
A) simply the middle value.
B) the difference of two middle values.
C) the simple average of two middle values.
D) multiplicative effect of the two middle most values.
8) the most commonly used measure of Central tendency is..
A) Geometric mean B) median C) Arithmetic mean D/ mode
9) The best measure of Central tendency is
A) Geometric mean B) quartile C) median D) mode
10) which of the following measure is the most difficult to compute ?
A) harmonic mean B) quartiles C) Mode D) Geometric mean
11) which of the following measures of Central tendency can have more than one value for a given set of observations?
A) Mean B) Median C) Mode D) both mean and mode
12) when weighted averages are used ?
A) when the data are put in the form of grouped frequency distribution
B) when data are not classified properly
C) when all the observations are not of equal importance.
D) either B or C above
13) if the set of observations contains both negative and positive values, which of the following measure of Central tendency cannot be considered ?
A) mode B) median C) Geometric mean D) arithmetic mean.
14) deciles divides the set of observations in how many part ?
A) 2 B) 10 C) 100 D) 4
15) how many deciles are more than 50 percentiles?
A) none B) 1 C) 2 D)all of the above.
16) which of the following measure of Central tendency satisfy a linear relationship between two variables?
A) mean B)median C)mode D) all of the above.
17) mode can be determined graphically using :
A) ogives B) histogram C) bar diagram D) all of the above.
18) Median can be calculated graphically using which of the following graph:
A) histogram B) pie charts C) ogives D) none.
19) percentiles are the values dividing a given set of observation into:
A) two parts B) ten parts C) 4 part D) 100 parts.
20) Given mean 25, mode 24, the median would be _____.
A) 24 B) 24.67 C) 25 D) 29
21) in a moderately asymmetrical distribution, the distance between the ___and the___ is about___ the distance between the___and the___
A) mean,median, 1/3, mean, mode.
B) mean, median,3, mean, mode.
C) mean,median, 1/3, median, mode
22) In a symmetrical distribution Mean ___Median___ Mode.
A) greater than, greater than
B) equal to, less than
C) equal to, equal to
D) less than, less than
23) The geometrical mean is the__ root of the product of all the measurements.
A) 5th B) nth C) (n+1)th D) (n-1)th.
24) the mode of the distribution is the value of that has the greatest of___.
A) concentration B) frequency C) either A or B above D) neither A nor B above.
25) the harmonic mean is the___of the arithmetic mean of the inverse of values.
A) reciprocal B) average C) median D) n.
26) the sum of divisions of individual observations is zero from:
A) mode B) median C) Arithmetic mean D) harmonic mean
27) Which average is affected most by extreme observations?
A) mode B) median C) Geometric mean D) harmonic mean.
28) in moderately asymmetrical distribution:
A)A.M> G.M> H.M
B) G.M>A.M>H.M
C) A.M<G.M<H.M
D) H.M<A.M>G.M
29) which of the following is the most unstable average:
A) Median B) Mode C) Geometric mean D) harmonic mean.
30) for dealing with qualitative data for the best average is:
A) Arithmatic mean B) mode C) median D) harmonic mean.
31) the positional measure of Central tendency is .
A) Geometric mean B) median C) harmonic mean D) Arithmetic mean
32) The geometrical mean of two numbers 8 and 18 shall be:
A) 16 B) 15 C) 14 D) 12
33) From a batch of 13 students who had appeared for an examination 4 students have failed. The marks of the successful candidates were 41, 57, 38,61,36, 35, 71,50, 40 calculate the median.
A) 40 B) 50 C) 38 D)cannot be determined
34) A motor car covered a distance of 50 miles four times. the first time at 50mph, the second at 20mph, the 3rd 40moh and the 4th at 25mph. calculate the average speed.
A) 29 B)33.75 C) 29.63 D) none.
35) A man gets 3 annual raises in salary. At the end of 1st year he gets an increase of 4%, at the end of second year an increase of 6% on his salary as it was at the end of the year, and at the end of the third year an increase of 9% on his salary as it was at the end of the third year. what is the average percentage increase?
A) 6% B) 6.3% C) 6.9% D) none.
36) A machine is assumed to depreciate 40% in value in the first year, 25% in the second year and 10% per annum for the next three years, each percentage being calculated on the diminishing value. what is the average percentage depreciation for 5 years?
A) 20% B)20.02% C) 21% D) 25%
37) Mohit travelled some distance by cycle at a speed of 15 km per hour. on return journey he travelled the same distance at a speed of 10 km per hour. what was his average speed per hour during entire journey?
A) 12.5 B) 13 C) 12 C) 15.
*** read the following information and answer the questions:
-> following is the data of the heights in inches of a group of student 61,62, 63,61, 63,64, 60, 65, 63, 64, 64, 66, 64
Now suppose that a group of students whose heights are 60, 96, 59, 68, 67 and 70 inches is added to the original group.
38) what is the mean of the new combined group ?
A) 67 B) 67.79 C) 63.5 D) 64
39) what is the median of the new combined group ?
A) 63.5 B) 63 C) 64 D) 69.
40) calculate the modal height of the students in the new combined group.
A) 63 B) 64 C) 65 D) 66
41) what is the difference between the mean of the original group and the mean of the combined group so formed by addition of a new students to the group ?
A) 4.02 B) t3.72 C) 4.72 D) none.
42) the mean of age of 100 person was found to be 32.02. later, it was discovered that the age 57 was misread as 27. then the correct mean is.
A) 32 B) 28 C) 32.32 D) 35.35.
43) the Arithmetic mean of 8,1,6 is.
A) 3 B) 4 C) 5 D) 6
44) the arithmetic mean of 8,1,6 is.
A) 5, B) 5.6 C) 6 D) 4.6.
45)* If 7, 4, 9 be the A M of three separate groups containing 6,2,5 observations respectively, then the AM of all the 13 observations is given by.
A) 7.29 B) 7.31 C) 7.00 D) 6.89
46) the algebraic sum of deviations of 8, 1, 6 from their Arithmetic mean is:
A) 1 B) 2 C) 0 D) none.
47) harmonic mean of 1, 8, 6 is.
A) 2 B) 3 C) 2.32 D) 3.32.
48) find out the mean of the numbers 2,5 8, 4, 9, 6, 71 is.
A) 6 B) 5 C) 5.5 D) none
49) Rani bought 6 rupees worth of orange from 5 markets at 15p, 20p, 25p, 30p and 50p per orange respectively. What is the average price of an orange?
A) 22p B) 28p C) 24p D) 25p.
50) what should be the average price, if she purchased 20 oranges from market from each market? (Take data from previous question)
A) 28p B) 24p C) 25p D) none.
51) the Arithmetic mean of 2 observations is 25 and their geometric mean is 15. the two observations are:
A) 25,25 B) 45,5 C) 35,15 D) 30,20.
52) If arithmetic mean is 26.8, median is 27.9, then what is the value of mode?
A) 29 B) 30.1 C) 31.1 D) 29.9 .
53) * the weighted Arithmetic mean of the four numbers 26, 128 ,12, 4 is 10.4. if the weight of the first three numbers are 1,3 and 4 respectively, find the weight of the fourth number.
A) 5 B) 6 C) 7 D) 8
54) find the Arithmetic mean of the number 3 ,5 ,7, 9,...47.
A) 24 B) 25 C) 27 D) 31
55) if a variable assumes the values 1,2,3,.... 10 with frequency 1,2,3,... 10 respectively, find the Arithmetic mean.
A) 6 B) 7 C) 8 D) 9
56) the weighted AM of 3, 5 and 10 with weight x, y, z respectively is known to be 8. what is the weighted AM if the weights are changed to 2x, 2y and 2z respectively?
A) 7 B) 8 C) 4 D) 16.
57) A variable x takes the values 10 and 20 with equal frequencies. find the Arithmetic mean.
A) 10 B) 15 C) 20 D) cannot be determined
58) a variable x takes all integral values from 1 to 10 with equal frequencies. find its Arithmetic mean.
A) 5 B) 6 C) 5.5 D) cannot be determined.
59) if the AM of 3,5 ,x ,12 ,17 be 9, find the value of x.
A) 5 B) 6 C) 7 D) 8
60) The algebraic sum of deviations of 25 observations measured from 55 is -55, find the Arithmetic mean of the observations.
A) 42.8 B) 50.8 C) 52.8 D) none
61) if a variable increases from 10 to 1000 at the same ratio in 10 years, find its value after 5 years.
A) 10 B) 100 C) 505 D) 200
62) the AM of two observations is 36 and their GM is 24. Then the HM
A) 14 B) 15 C) 16 D) 18.
63) find the GM of the following: 3, -2, 4, 0, 5.
A) 2 B) 3 C) 1 D) cannot be determined.
64) the HM of -3,2,4,0, -5 is.
A) 1 B) 2 C) 3 D) cannot be determined.
65) the AM of the following -2, 3, 0, 5, 4 is.
A) 1 B) 2 C) 3 D) cannot be determined
66) what is the difference between the median and mode of the following observation 4, 7, 10 ,7,9, 15, 12, 7, 9, 6.
A) 1 B) 2 C) 0.5 D) 1.5
67) find the mode of the following 2, 7, 4, 3, 6
A) 2 or 3 or 4 or6 B) 3 or 7 C) 4 D) it does not exist.
68) For the following observations, 500, 525, 475, 480, 520, 2593, regarding monthly income for 6 persons, which measure of Central tendency, would be appropriate?
A) Arithmetic mean B) Geometric mean C) median D) none.
69) in a set of values of variable X, the smallest value is 0.9. and the highest is 1.9. which of the following 5.2, 1.3, 0.7, - 0.3. is a possible value of the mean ?
A) 1.3 B) 0.7 C) 5.2 D) -0.3.
70) The arithmetic mean of a valiable Y is 10. find the mean of variable 5Y - 10.
A) 50 B) 40 C) 25 D) 30.
71) two variable x and y are given by y=2x - 11. if the median of x be 30, find the ratio of the median of y to that of x.
A) 4:3 B) 49:13 C) 49:30 D) 41:30.
72) If u = 5x, GM of x is 1 and HM of x is 0.4, the ratio of GM and HM of u.
A) 5:2 B) 2.5:2 C) 5:1.5 D) 3:1
73) if for a symmetrical distribution 1st Quartile= 20 and 3rd Quartile=30, find the median.
A) 20 B) 25 C) 30 D) 15
74) how many deciles lie below the first quartile ?
A) 5 B) 25 C) 2 D) none.
** for the statements given state the appropriate type of average to be used:
75) the distribution has open-end classes.
A) mode B) median C) either mode or median D) Arithmetic mean
76) marks obtained in Statistics by the student in an examination.
A) mode B) the Arithmetic mean C) median D) harmonic mean.
77) the size of shoes sold in a shop
A) Median B) quartiles C) Mode D) Geometric mean.
78) A frequency distribution having open-end classes.
A) mode B) Arithmetic mean C) harmonic mean D) median.
79) different rates of depreciation charges on diminishing balance.
A) arithmetic mean B) Geometric mean C) harmonic mean D) all of the above.
80) speeds is several journeys when the distance covered is the same in each journey.
A) Arithmetic mean B) Geometric mean C) harmonic mean D) all of the above.
81) speeds in several when the time taken is same in each journey.
A) Arithmetic mean B) harmonic mean C) both A and B) above D) neither A nor B above.
82) when distribution pattern has to be studied at varying level.
A) Arithmetic mean B) median C) mode D) geometric mean
83) when it is desired the sampling variability should be least.
A) Median B) Mode C) quartile D) arithmetic mean.
84) when it is desired that the sum of the deviation from the average should be least.
A) Geometric mean B) Arithmetic mean C) median D) mode
85) inference about population mean has to be drawn.
A) Median B) Mode C) deciles D) Arithmetic mean.
86) the distribution has wide range of variations.
A) Mode B) Arithmetic mean C) harmonic mean D) median
87) the quantities are in ratios.
A) harmonic mean
B) Geometric mean
C) Arithmetic mean
D) either A or B above.
88) when variability has also to be calculated.
A) Geometric mean B) quartile C) percentile D) arithmetic mean.
89) The values changing at a cumulative rate have to be found
A) harmonic mean B) Geometric mean C) Arithmetic mean D) either A or C above
90) which of the following statements are TRUE?
A) mean is it dependent of origin, but depends upon the scale.
B) mode is the value of the largest observation in the series.
C) the lower quartile of the distribution is N/4 and the upper quartile is 3N/4 D) none
91) If a variable assumes n values a, ar, .... arⁿ⁻¹ with (r > 1) equal frequencies then find the arithmetic mean of the observations.
A) a(rⁿ -1)/(r-1). B) a(rⁿ -1)/n(r-1).
C) a(rⁿ -1)/(1-r). D) none.
92) the weekly wages of 5 labourers are ₹40, 60, 36, 45, 25. calculate their AM.
A)₹40 B)₹52.14 C)₹41.20 D)₹42.20.
93) find the Arithmetic mean of 14,16 ,19,25 ,21.
A) 18 B) 19 C) 20 D) 21
94) find the geometric mean and harmonic mean of the numbers 1, 9, 81.
A) 9,3,61 B) 3,2,55 C) 9,2,55 D) 9,3,54
95) If AM =25, HM=9, then GM is
A) 15 B) 20 C) 21 D) 90
96) find the geometric mean of 2, 9, 12.
A) 2 B) 6 C) 9 D) 7
97) find the geometric mean of 6, 24 ,12.
A) 11 B) 12 C) 13 D) 18
98) calculate the harmonic mean of 4 numbers is 3,6 ,24 and 48.
A) 6.0 B) 7.8 C) 7.1 D) 6.9
99) calculate Geometric mean of the four numbers: 4,6, 12,72.
A) 6 B) 18 C) 36 D) 12.
100) calculate the mean of the numbers: 24, 72, 108, and 144.
A) 78 B) 87 C) 98 D) 89.
101) find harmonic mean of the following 1,1/2,1/3...1/n.
A) 2/{n(n+1)} B) 2n/(n+1)
C) 2/(n+1) D) none.
102) find harmonic mean of the following 1,1/3,1/5,...1/(2n-1).
A) 1/(n+1) B) 1/(n-1) C)3/n D) 1/n.
103) find the median of the following numbers 7,2,5, 9,6.
A) 5 B) 6 C) 5.5 D) 6.5.
104) find the median of the following 8,3,11, 7 ,12,6,9.
A) 6 B) 7 C) 8 D) 11
105) the median of the set of the following numbers 33,86,32, 80, 48, 70.
A) 48, B) 32 C) 33 D) 68. E) none
106) find the mode of the following numbers: 5, 3, 37, 5, 9, 3, 8, 5.
A) 5 B) 3 C) can't be determined D) n
107) the mode of the following: 4, 3, 2,5, 3 ,4,5, 3, 7, 3, 2,6.
A) 2 B) 3 C) 4 D) none.
108) find the mode and median of the following numbers: 25, 1275, 748, 162, 967, 162, 162.
A) 162, 554 B) 162, 455 C)162 748 D) n.
109) find the median of the following numbers: 94, 33,86, 68,32 80,48,70.
A) 68 B) 69 C) 70 D) 71
110) the median of the following numbers: 79,82, 36,38, 51,72, 68,70, 64, 63.
A) 64 B) 65 C) 66 D) 63.
111) find the mean and median and mode: 4,3,2,5,3,4,5,2,7,3,2,1.
A) 3,3 B) 3.33, 3.33 C) 3.33,3 D) n.
112) find the mean and mode of the following number 7,4,10, 15, 7,3,5, 2, 9, 12.
A)7,7,4 B) 7,4,7 C) 7,7 D) 7.4 ,7.4.
113) find the median and mode of the number 4, 10, 7, 15, 7, 3, 5, 3, 7.
A) 7,7 B) 7.4,7.4 C) 7,7.4 D) 7.4 ,7.
114) Find the mean, median and mode of the following numbers: 7, 4, 3, 5, 6,3 ,3, 2, 4 ,3,4 3, 3,4, 4, 3,2, 2, 4,3,5 ,4,3, 4 , 3,4, 3, 1,2,3.
A) 3.33, 3,3 B) 3, 3,3 C) 3.47,3,3 D) 3.47, 3.47,3.
115) find the quartiles of the values: 35, 30, 48, 40, 25, 36, 45.
A) 30, 35, 41 B) 30, 36, 45 C) 29, 36, 45 D) none of the above.
116) Find the deciles of the following numbers: 50, 80,60, 30,40, 10, 45, 20, 25, 75, 55, 65,35, 52,44, 38,63, 34, 46.
A) 20, 30, 35, 40 ,45, 50 ,55, 63,75.
B) 20, 30, 33,40, 45,50,55,65.
C) 20, 30, 35,40, 45,50,55,60,65 D) n
117) the number 3.8, 5.8, 7.9 and 4.5 have frequencies x, x+2, x-3 and x+6 respectively. If the Arithmetic mean is 4.876, find the value of x.
A) 3 B) 4 C) 5 D) 6.
118) A sample of size 50 has mean 54.4 and another sample of size 100 mean 50.3. if the two samples are pooled together. find the mean of the combined sample.
A) 50 B) 51 C) 51.7 D) none
119) if the mean and mode of a certain set of a numbers be 60.4 and 50.2 respectively. find approximately the value of the median.
A) 55 B) 56 C) 57 D) 58.
120) if the mean of some of the observations be 25 and their HM is 9, find their GM.
A) 15 B) 9 C) 18 D) 24.
121) the monthly incomes of five labourers are ₹150, ₹140, ₹165, ₹ 170 and ₹180. calculate the Arithmetic mean and geometric mean.
A) ₹160,₹160.30 B) ₹161, ₹160.30.
B) ₹160.30, ₹160.30. D) none.
122) the monthly income of six labourers are ₹70, 42, 85,75, 68,55. calculate the AM and GM.
A) 65, 64.21 B) 65,65 C) 65.83,64 D) 65.83 64.21
123) the mean of 20 observations is 85; but it was later found that the two observations were wrongly read as 75 and 70 instead of 57 and 60. Find the actual mean.
A) 85 B) 83 C) 83.6 D) none.
124) the weighted Arithmetic mean of first n natural numbers whose weights are equal to the corresponding numbers is equals to.
A) (2n-1)/3 B)(2n+1)/6 C) (2n+1)/3 D) n.
125) The mean wage of 100 workers working in a factory running two shifts of 60 and 40 workers respectively is ₹38. The mean wage of 60 labourers working in the morning shift is ₹40. find the mean wage of labourers working in the evening shift.
A) ₹30 B) ₹38 C) ₹41 D) none.
126) the algebraic sum of the divisions of 25 observations measured from 45 is - 55; find the AM of the observation.
A) 32.8 B) 52.2 C) 39.75 D) 42.20.
127) the mean of 20 observations is 16.5. if by mistake one of the observation was copied 12 instead of 21. find the correct value of mean.
A) 16.5 B) 16.95 C) 17 D) 17.5
128) The mean marks of 100 students was found to be 40. later on it was discovered that a mark 53 was misread as 83. find the correct mean mark.
A) 39 B) 40 C) 39.5 D) 39.7.
129) the mean weekly salary paid to 77 employees in a company was ₹78. the mean salary of 32 of them was ₹75 and the other 25 had a mean salary of ₹82. what was the main salary of the remaining ?
A) 77.80 B) 78.87 C)78.70 D) 78.90
130) the mean annual salary paid to all employees of a company was ₹5000. the mean annual salaries paid to male and female employees were ₹5200 and ₹4200 respectively. determine the percentage of males and females employed by the company.
A) 60% ,40% B) 80% ,20 C) 50%,50% D) none.
131) the mean monthly salary paid to all employees in a certain company was ₹600. the mean salaries paid to male and female employees were ₹620 and ₹520 respectively. Obtain the ratio of male and female employees in the company.
A) 1:1 B) 1:4 C) 3:2 D) 4:1
132) the mean of marks scored by 30 girls of a class is 44%. The mean marks of 50 boys is 42%. find the mean for the whole class.
A) 42.00% B) 43.85% C) 44.25% D) 42.75%.
133) a set of 20 values have mean 54. Another set of values have mean 60. if the combined mean is 56, how many values are there in the letter set ?
A) 8 B) 9 C) 10 D) 12.
134) find the AM of the following distribution:
Weight: 100 110 120 130 140
Number: 15 20 25 30 10
A) 110 B) 100 C) 120 D) 130
135) calculate the Arithmetic mean and the mode from the following:
X: 1 2 3 4 5 6 7 8 9
F: 7 11 16 17 26 31 11 1 1
A) 4.59,6 B) 6, 4.59 C) 6,6 D) 4.59, 4.59
136) The average weight of the following frequency distribution is 117 lbs. find the value of x.
X: 100 110 120 x+25 140
F: 1 4 2 2 1
A) 110 B) 100 C) 120 D) 105.
137) find the mode from the following distribution:
Mark number of candidates
01 -05 7
06 -10 10
11-15 16
16- 20 32
21-25 24
26-30 18
31-35 10
36-40 5
41-45 1
A) 18 B) 18.83.C) 17.83 D) n
138) The mean of the following data is 67.45. find the missing frequencies.
Height number of students
60- 62 5
63- 65 18
66-68 a
69-71 b
72-74 8
Total 100
A) 40,29 B) 27,42 C) 42,27 D)38,31
139) from the following Cumulative distribution of marks of 22 students, the arithmetic mean, median and mode of the distribution would be;
Marks number of students
below 10 3
below 20 8
below 30 17
below 40 20
below 50 22
A) 23,23,24 B) 23.18, 20.33, 24 C) 23.33, 23.18, 24.83 D) 23.81, 23.33, 24.33.
140) calculate the first and third quartiles for the following data:
class-limits frequency
10- 19 5
20 -29 9
30 - 39 14
40- 49 20
50- 59 25
60 -69 15
70-79 8
80 -89 4
A) 37.36, 60.83 B) 37, 61 C) 37.63, 60.38 D) none.
141) Using suitable formula calculate the mean and the median from the following data:
mid value frequency
115 6
125 25
135 48
145 72
155 116
165 60
175 38
185 22
195 3
A) 153 ,153 B) 153.64, 153.8 C) 152.4 ,153.8 D) 153.64, 152.8
142) the median and mode of the following Cumulative data is:
Annual sales(₹'000) frequency
less than 10 4
less than 20 20
less than 30 35
less than 40 55
less than 50 62
Less than 60 67
A) 29000, 32778 B) 32778,49000
C) 29978, 34787 D) 30000, 33000
143) what is the value of a if the mean of the following distribution is 38 ?
Marks number of student
10 8
20 11
30 20
40 25
50 a
60 10
70 3
A) 17 B) 18 C) 19 D) 20
144) the value of 45th and 57th percentiles for the following data on marks obtained by 100 students
Marks number of students
20-25 10
25-30 20
30-35 20
35-40 15
40-45 15
45-50 20
A) 33.75, 37.33 B) 35.73, 37.35
C) 33.75, 43.33 D) 33.75, 34.33
145) The median the mode of the following daily wages distribution of 230 workers are known to be ₹33.50 and ₹34.00 respectively. Three frequencies values from the table are, however missing. Find these missing values.
Wages number of workers
00-10 4
10-20 16
20-30 a
30-40 b
40-50 c
50-60 6
60-70 4
A) 20,40,100 B) 60,100, 40 C) 50,100, 50 D) 50,110, 40.
146) find the median and mode of the following frequency distribution
No. of days absent No. of students
Less than 5 29
less than 10 224
Less than 15 465
Less than 20 582
less than 25 634
less than 30 644
Less than 35 650
Less than 40 653
Less than 45 655
A) 12, 11 B) 12, 14, 11 C) 12.14, 11.35 D) 12.59, 11.35
147) find the missing frequencies, if the first quartiles of the following data is 21.5.
class frequency
10-15 24
15-20 a
20-25 90
25-30 122
30-35 a
35-40 56
40-45 20
45-50 33
Total 460
A) 60,55 B)61,54 C) 64,51 D) 54,61
148) the following table gives the distribution of 100 families according to expenditure. If mode of the distribution is 24, find the missing frequencies, a, b.
expenditure Number of families
00- 10 14
10-20 a
20-30 27
30-40 b
40-50 15
A) 20,24 B)21, 23 C) 22, 22 D)23, 21
149) following is the distribution of the marks in economics by 50 students. If 60% of the students pass their test, find the minimum marks obtained by a pass candidate.
Marks more than No.of students
0 50
10 46
20 40
30 20
40 10
50 3
A) 20 B) 25 C) 30 D) 28
150) you are given below a certain statistical distribution, calculate the most suitable average.
value frequency
less than 100 40
100-200 89
200-300 148
300-400 64
400 and above 39
A) median= 240 B) median= 251.22 C) mean =241 D) none
EXERCISE-2
1) x and y are related bye x-y-10= 0 and mode of x of is 23 then mode of y is
A) 20. B) 13. C) 3. D) 23
2) A man travels at a speed of 20Km/hr and then returned at a speed of 30Km/hr. His average speed the whole journey is:
A)25. B) 24.5. C) 24. D) none
3) A student of obtained mean of 100 observations as 40. it was later discovered that he copied wrongly as 50 instead of 40. Correct mean is
A) 5 B) 7 C) 20 D) none
4) median of 13, 8, 11, 6, 4, 15, 2, 18 is:
A) 5. B) 8. C) 11. D) 9.5
5) The sum of the squares of deviations of a set of observations has the smallest value, when the deviation are takes from
A) A.M. B) H.M. C) G.M. D) none
6) Find the correct relation
A) A.M≥ G.M≥ H.M
B) G.M>A.M>H.M
C) G.M≥A.M≥H.M
D) A.M>G.M>H.M
7) if the A.M and H.M of two numbers are 5, 3.2 thenG. M is
A) 4.05. B) 16. C) 4. D) 4.10
8) ---- are used for measuring Central tendency, dispersion, skewness
A) median b) percentile
C) Percente D) Quartile
9) An aeroplane live from A to B at the rate of 500km/hr and comes back from B to A at the rate of 700 km/hr average speed is:
A) 600 b) 583.33 c) 591,61 d) 620
10) For a mondorately skewed distribution, which is holda
A) mean- med=3(med- mode)
B) med- mode=3(mean-med)
C) mean-mode=3(mean- med)
D) mean- med=3(mean- mode)
11) --- and--- are called ratio averages
A) H.M & G.M B) H.M & A.M
C) A.M & G.M. D) NONE
12) Extreme values have --- effect on mode.
A) high. B) low. C) no. D) none
13) The mean salary for a group of 40 female workers rupees 5200 per month and that for a 60 male workers is ₹6800 per month combined salary is
A) 6160 b) 6280 c) 6890 d)6920
14) If there are two groups with 75 and 65 as harmonic mean and containing 15 and 13 observations
a) 70. b) 80 c) 70.35. d) 69.48
15) the geometric mean of of 4, 6 and 8 is
A) 4.77 b)5.32 c) 16.14 d) 15.77
16) GM is a better measure than others when
A) ratios and percentage are given
B) interval of scale is given
C) both A and B
D) either A and B
17) the median x,x/2,x/3,x/5 is 10 find x where x>0
A) 24. B) 32. C) 8. D) 16
18) The average salary of 50 man was ₹80 but it was found that salary of 2 of them were ₹46 and. ₹ 28 which was wrongly taken as 64 and 82. The revised average salary
A) 80 b) 78.56 c) 85.26 d) 82.32
19) if A be the A.M of two positive unequal number X and Y and G be their GM then
a) A<G b) A>G c) A≤ G d) A≥ G
20) when mean and mode is 3.57 and 2.13 then median is
A) 3.09. B) 5.01. C)4.01. D) none
21) The H. M of 1/2,1/3,1/4,..1/n
A) 1/(n+1) b)2/(n+1)
c) (n+1)/2 d) 1/(n-1)
22) the mean weight of 15 boy is 110 kg the mean weight of five of them 100 kg. and another 5 is 125kg. the mean weight of rest boys is
A)120 b) 105. C) 115. D) none
23) In a class of 11 students 3 students were where failed in a test. 8 students who passed secured 10 ,11,20,15,12,14,26 and 24 marks; median is
A) 12. B)15. C) 13. D)13.5
24) a body travels at a speed of 20 km/hr and returned at Quicked speed. if her average speed of the whole journey is 24km/hr. Speed when return
A) 25. B) 30. C) 35. D) 38
25) mean of the the variable x be 50, then mean of u=10+5x will be
A) 250 b) 260 c) 265 d) 273
26) if the difference between mean and mode is 6. then the difference between mean and the median will be
A) 63 b) 31.5 c) 21 d) none
27) if A. M and GM between two number is 16 then HM is
A). 64. B) 4. C) 16. D) 40
28) the average of 5 items is six and average of 3 items is 8. average of the remaining 2 is
A) 4. B) 5. C) 3. D) 3.5
29) X: 11 13 15 19
F: 33 35 39 46
Median is:
A) 11. B) 13. C) 15. D) 19
30) the average age of 10 students was 20 years. the average age increased by 2 years when years when two new students joined the group. Then average age of two new students:
A) 22. B) 30. C) 44. D) 32
31) GM of three observations 40, 50 and x is 10. then X is
A) 2. B) 4. C) 1/2. D) none
32) the mean of first three term is 14 and mean of next two term is 18, then mean of all 5 terms is:
A). 14.5. B) 15. C) 14. D) 15.6
33) mean salary of a group of 50 is ₹ 5850, later it is discovered that the salary of one employee has been wrongly taken care ₹8000 instead of Rs 7800. find correct mean.
A) 5854 b)5846 c)5650 d) none
34) If the mode of a data is 18 and mean is 24, the median is:
A) 18. B) 24. C) 22. D) 21
35) for data on Frequency distribution of 70,73,49,57,56,44, 56, 71, 65, 62,60, 50, 55, 49, 63, and 45. If we assume Class length as 5, the number of class interval:
A) 5. B) 6. C) 7. D) 8
36) The point of intersection of the 'less than' and 'more than' ogives correspond to
A) mean b) Mode
c) median d) 10th percentile
37) which of the following measure of Central tendency cannot be calculated by graphical method
A) mean. b) mode
c) median d) quartile
38) GM of 8, 4, 2 is:
A) 4 b) 2 c) 8 d) none
39) The average age of 15 students of a class is 15 years. out of them the average of 5 Students is 14 years. And that of 9 Students is 16 yrs. the age of 15th students is:
A) 11. Bb) 14. C) 15. D) none
40) In normal distribution mean, medium and mode are
A) equal b) not equal
C) zero d) none
41) the price of average value can be find graphically
A) mode, median b) mean,mode
C) mean and median d) N
42) find the statement
A) median is based on all the observations
B) the mode is the mid value
C) median is 2nd quartile
D) mode is 5th Decile.
43) x: 2 4 6 10 p+5
F: 3 2 3 1 2
If the mean is 6, then P is:
A) 4. B) 6. C) 8. D) 7
44) A random variable X has uniform distribution on the interval (-3,7). The mean of the distinction is
A) 2. B) 4. C) 5. D) 6
45) If AM and GM of two numbers are 10,8 then HM is
A) 9. B) 8.9. C) 6.4. D) none
46) The HM of two numbers is 4 and AM is A. And GM is G satisfy the equation 2A+G²= 27. then the numbers are
A) 1,3 b) 9,5. C) 6,3. D) 12,7
47) in a class of 50 students, 10 have failed and their average marks is 2.5. the total marks secured by entire class were 281. The average marks who have passed is:
A) 5.32 b)7.25 c) 6.4. D) none
48) If mean and geometric mean of two numbers are 30 and 24 find the the number the number 24. find the numbers.
A) 36,24 b)30,30 c)48,12 d) N
49) For moderately skewed distribution of marks of 200 students the mean and mode are 55.60 and 46. what is median.
A) 55.5 b) 60.5. C). 52.4 d) N
50) mean for the data 6,4,1, 6, 5, 10, 3 is 5 when each observation is added by 2 . what is the mean of data
A) 5. B) 6. C) 7. D) 10
51) that the average of 10 observation is 14.4. if the average of first 4 observations is 16.5. the average of remaining six observation is:
A)13.6. B) 13. C) 13.2 d) 12.5
52) the ordering of particular design of a cloth... size be more appropriate
A) medium b) mean c)mode d) all
53) the rates of Return from the shared are 100%, 200%, 400%. The average rate of return will be
A)350 b)233.33%c)200% d)300%
54) If GM is 6 AM is 6.5 then AM
a) 5.54 b) 0.14. C) 0.92 d) none
55) A person purchases 5 rupees worth of eggs from 10 different markets. you are to find the average number of eggs per ₹. purchased from all the markets taken together the suitable average in this case is:
A) AM. B) GM. C) HM. D) none
56) Shoe-size of most of the people in India is number which measure of Central tendency values does it represent
a) mean b) 2nd quartile
c) 7th Decile d) mode
57) If a constant 5 is added to each of the observation of a set, the mean is:
A) increased by 5
b)decreased by 5
c) 5times the original mean
d) not effected
58) If each number is multiplied by 10. the new mean is
A) remains the same
B) is 10 time the original mean
C) is one-tenth the original mean
D) is increased by 10.
59) If each number multiplied by 10. the median is
A) not affected
B) 10 times the original median
C) one tenth of the original value
D) increased by 10
60) extreme value has no effect on....
A) average b)median c) GM d) HM
61) the median of 11,7, 6,9,12,15, 19 is
A) 9. B) 12. C) 15. D) 11
62) For a negatively skewed distribution, the correct inequalities is....
A)mode<median B) mean<median
C) mean<mode d) none
63) Mean is a measure of.....
A) location b) dispersion
C) Correlation. D) regression
64) which is a measure of Central tendency.
A) median.b) SD d) MD e) QD
65) GM is better than other means when the data are
A) positive as well as negative.
B) ratio or percentage c) binary
D) Interval Scale.
66) the correct relationship between AM,GM and HM
A) AM=GM=HM B) GM≥AM≥HM
C) HM≥GM≥AM D) AM≥GM≥HM
67) which mean is most affected by Extreme values
A) GM. B) HM. C) HM d) mean
68) the value in a series most frequent is called
A) Mean b) Median C) Mode d)HM
69) find the true:
A) mean has affect on extreme scores
B) median has an effect on extreme scores.
C) extreme scores have effect on mean.
D) extreme scores have effect on median.
70) if the Arithmetic mean of two numbers is 5. one of them is 3, other is
A) 3. B) 5. C) 7. D) 10
71) the sum of the squares of the deviation about mean is
A) zero b) maximum
C) minimum d) all the above
72) If mean of x is 25, the minimum be:
A) summation of (x-27)
B) summation of ((x-25)²
C) summation of (x-22)²
D) summation of (x+25)²
73) the mean for a se of data obtained by assigning each data value a weight that reflects its relative importance within the set is called
A) GM b) HM
C) weighted mean
D) combined mean
74) any measure indicating the the centre of a set of data, arranged in an increasing or decreasing order of magnitude, is called a measure of:
A) skewness. B) symmetry
C) Central tendency d) dispersion
75) Scores that differ from the measured of Central tendency are called
A) Row scores. B) the best scores
C) extreme scores d) Z- scores
76) the measure of Central tendency listed is
A) the row score b) mean
C) rangr d) standard deviation
77) the total of all the observations divided by the number of observation is called
A) AM b) GM. C) median d) HM
78) while computing the AM of a frequency distribution, the each value of a class considered equal to:
A) class mark B) lower limit
C) upper limit.
D) lower class boundary
79) change of origin and scale is used for:
A) AM. B) GM c) weighted mean
D) lower and upper upper
80) the sample mean is :
A) parameter B) statistics
C) variable d) constant
81) the AM. is highly affected by
A) moderate values
b) extremely small values
c) odd values d) extremely large
82) If a constant value is added to every observation of data, then Arithmetic mean is obtained by
A) subtracting the constant
B) adding the constant
C) multiplying d) dividing
83) step deviation method or coding method used to:
A) Arithmetic mean B) GM
C) weighted mean D) HM
84) if the AM of 20 is 10, then sum of those 20 is
A) 10. B) 20. C) 200. D) 20+10
85) 10 families have an average of two boys . how many boys do they have together.
A) 2. B) 10. C)12. D) 20
86) the sample mean of first n natural numbers
A) n(n+1)/2. B) (n+1)/2
C) n/2. D)(n-1)/2
87) when the values in a series are not equal importance we say
A) AM. B) GM
C) weighted mean d) mode
88) when all the values in a series occur the equal number of times, then it is is not possible to calculate
A) AM b) GM. C) HM
D) Weighted mean
89) arithmetic mean of 10 items is 4 and of 5 items is 10. find combined mean.
A) 4. B) 5. C) 6. D) 90
90) the midpoint of the values after they have been ordered from the the smallest to the largest or the largest to the smallest called
A) mean. b) median
C) first quarterly d) 3rd quartile
91) the first step in calculating the median of a descrete variables is to determine
A) cumulative frequencies
B) relative weight
C) relative frequencies d) array
92) the suitable average for quartile data is :
A) mean b)Median c) Mode d) GM
93) extreme scores will have the following effect on the median of an examination
A) they may have no effect on it
B) they may tend to raise it
C) they may tend to lower it d) N
94) we must arrange the data before Calculating
A) mean b)median c)mode d) GM
95) If the smallest observation in a data is decreased, the average which is not affected is:
A) mode b)median c) mean d)HM
96) If the data contains an extreme value, the suitable average is:
A) mean. b) median
C). Weighted mean. D). GM
97) sum of absolute deviation of the values is less when deviations are taken from
A) mean b) median c) mode d) N
98) the values of the variates that divide a set of data into to four equal parts after arranging the observation in ascending order of magnitude is
A) quartile. B) Decile
C) percentiles d) none
99) the middle value of ordered series is called
A) median. B) 5th Decile
C). 50th percentiles. D) all
100) the mode of the observation is that value of the variate for which frequency is
A) minimum b) maximum
C) odd number d) even number
101) Suitable average for averaging the shoe size for children is
A) mean b) mode c)median d)GM
102) A measurement that corresponds largest frequency in a set is
A) mean b) median
C) upper Quartile d) percentile
103) which average method cannot calculated for 2,2, 4,4,6 ,8,8, 10,10
A) mean b) median c) mode d) all
104) Mode of the series 0, 0, 0, 2,2 3,8, 10
a) 0 b) 2 c) 3 d) no mode
105) a distribution with two modes is called
A) uni modal b) bimodal
C) multimodal d) normal
106) the moal letter of the word STATISTICS
A) S. B) T. C) Both S and I
D)) both S and T
107) taking the relevant root of the product all non-zero and positive values are called
A) AM. B) GM
C). HM. D) combined mean
108) the best average in percentage rates and ratio is
A) AM. B) lower and upper Quartile. C) GM. D) HM
