Math questions on Mean, Mode and Median:

Ques. Which of the following average is most affected of extreme observations?
(a) Mode
(b) Median
(c) Arithmetic mean
(d) Geometric mean

Ans. (c)

Ques. The mean of 5 numbers is 18. If one number is excluded, their mean becomes 16. Then the excluded number is
(a) 18
(b) 25
(c) 26
(d) 30

Ans. (c)

Ques. What is the arithmetic mean of the following data?

Marks	20-29	30-39	40-49	50-59	60-69	70-79
Frequency	5	11	18	22	16	8

(a) 16.5
(b) 51.6
(c) 54.5
(d) 16.6

Ans. (b)

Ques. Mode of 0,3,5,6,7,9,12,0,2 is
(a) 6
(b) 0
(c) 3
(d) 5

Ans. (b)

Ques. The average weight of students in a class of 35 students is 40 kg. If the weight of the teacher be included, the average rises by ½ kg; the weight of the teacher is
(a) 40.5 kg
(b) 50 kg
(c) 41 kg
(d) 58 kg

Ans. (d)

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Ques. For a symmetrical distribution Q₁ = 25 and Q₃ = 45, the median is
(a) 20
(b) 25
(c) 35
(d) None of these

Ans. (c)

Ques. If the mean of 3, 4, x, 7, 10 is 6, then the value of x is
(a) 4
(b) 5
(c) 6
(d) 7

Ans. (c)

Ques. Find the combined arithmetic mean of two samples of sizes 6 and 4 respectively whose means are 15 and 25.
(a) 20
(b) 19
(c) 40
(d) 21

Ans. (b)

Ques. The mean proportional between 1.4 gms and 5.6 gms is
(a) 28 gms
(b) 2.8 gms
(c) 3.2 gms
(d) None of these

Ans. (b)

Ques. A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s and seven 10’s. The mode of this set of numbers is
(a) 6
(b) 7
(c) 8
(d) 10

Ans. (c)

Ques. If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is
(a) 30
(b) 30.1
(c) 29
(d) 31

Ans. (d)

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Ques. For a normal distribution if the mean is M, mode is M_o and median is M_d, then
(a) M > M_d > M₀
(b) M < M_d < M₀(c) M = M_d M₀
(d) M = M_d = M₀

Ans. (d)

Ques. The mean of 5 numbers is 18. If one number is excluded, their mean becomes 16. Then the excluded number is
(a) 18
(b) 25
(c) 26
(d) 30

Ans. (c)

Ques. If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately
(a) 25.5
(b) 24.0
(c) 22.0
(d) 20.5

Ans. (b)

Ques. In case of an even number of observations which of the following is median ?
(a) Any of the two middle-most value
(b) The simple average of these two middle values
(c) The weighted average of these two middle values
(d) Any of these

Ans. (b)

Ques. The A.M. of a 50 set of numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, the A.M. of the remaining set of numbers is
(a) 38.5
(b) 37.5
(c) 36.5
(d) 36

Ans. (b)

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Ques. The central value of the set of observations is called
(a) Mean
(b) Median
(c) Mode
(d) G.M.

Ans. (b)

Ques. The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are
(a) 2 and 9
(b) 3 and 8
(c) 4 and 7
(d) 5 and 6

Ans. (c)

Ques. Which of the following is not a measure of central tendency
(a) Mean
(b) Median
(c) Mode
(d) Range

Ans. (d)

Ques. The harmonic mean of 4, 8, 16 is
(a) 6.4
(b) 6.7
(c) 6.85
(d) 7.8

Ans. (c)

Ques. The total expenditure incurred by an industry under different heads is best presented as a
(a) Bar diagram
(b) Pie diagram
(c) Histogram
(d) Frequency polygon

Ans. (b)

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Ques. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new set
(a) is increased by 2
(b) is decreased by 2
(c) is two times the original median
(d) Remains the same as that of the original set

Ans. (d)

Ques. The arithmetic mean between two numbers is A and S is the sum of n arithmetic means between these numbers, then
(a) S = nA
(b) A = nS
(c) A= S
(d) none of these

Ans. (a)

Ques. If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately
(a) 25.5
(b) 24.0
(c) 22.0
(d) 20.5

Ans. (b)

Ques. Which of the following, in case of a discrete data, is not equal to the median
(a) 50th percentile
(b) 5th decile
(c) 2nd quartile
(d) Lower quartile

Ans. (d)

Ques. Which of the following is not a measure of central tendency
(a) Mean
(b) Median
(c) Mode
(d) Range

Ans. (d)

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Ques. The mean weight per student in a group of seven students is 55 kg If the individual weights of 6 students are 52, 58, 55, 53, 56 and 54; then weights of the seventh student is
(a) 55kg
(b) 60kg
(c) 57kg
(d) 50kg

Ans. (c)

Ques. _____ is the mean proportional between 12x² and 27y².
(a) 18xy
(b) 81 xy
(c) 8 xy
(d) 19.5 xy

Ans. (a)

Ques. In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class are 72, then what are the average marks of the girls
(a) 73
(b) 65
(c) 68
(d) 74

Ans. (b)

Ques. In a moderately asymmetrical distribution the mode and mean are 7 and 4 respectively. The median is
(a) 4
(b) 5
(c) 6
(d) 7

Ans. (b)

Ques. A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than
(a) 60%
(b) 65%
(c) 80%
(d) 90%

Ans. (a)

Ques. In a moderately asymmetrical distribution the mode and mean are 7 and 4 respectively. The median is
(a) 4
(b) 5
(c) 6
(d) 7

Ans. (b)

Ques. ______ always lies in between the arithmetic mean & mode.
(a) G.M.
(b) H.M.
(c) Median
(d) G.M. and H.M.

Ans. (c)

Ques. A school has four sections of chemistry in a class having 40, 35, 45 and 42 students. The mean marks obtained in chemistry test are 50, 60, 55 and 45 respectively for the four sections, the overall average of marks per students is
(a) 53
(b) 45
(c) 55.3
(d) 52. 25

Ans. (d)

Ques. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new set
(a) Is increased by 2
(b) Is decreased by 2
(c) Is two times the original median
(d) Remains the same as that of the original set

Ans. (d)

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Ques. The central value of the set of observations is called
(a) Mean
(b) Median
(c) Mode
(d) G.M.

Ans. (b)

Ques. The median of 10, 14, 11, 9, 8, 12, 6 is
(a) 10
(b) 12
(c) 14
(d) 11

Ans. (a)

Ques. Find the median wage of the following persons.

Wage (in Rs)	20-30	30-40	40-50	50-60	60-70
No. of persons	3	5	20	10	5

(a) 45.75
(b) 50
(c) 46.75
(d) 45

Ans. (c)

Ques. What is the geometric mean of 2,4and 8?
(a) 4
(b) 6
(c) 5
(d) 7

Ans. (a)

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Ques. Mean marks of 150 students were found to be 50.Later it was found that a score of 87 was misread as 78.What is the correct mean?
(a) 49.9
(b) 59
(c) 50.09
(d) None of these

Ans. (c)

Ques. What is the range of the following data?