Class 11 Mathematics Statistics MCQs Set 01

Question. The arithmetic mean of the series \( ^nC_0, ^nC_1, ^nC_2, \dots, ^nC_n \) is
(a) \( \frac{2^n}{(n+1)} \)
(b) \( \frac{2^n}{n} \)
(c) \( \frac{2^{n-1}}{(n+1)} \)
(d) \( \frac{2^n}{(n-1)} \)
Answer: (a) \( \frac{2^n}{(n+1)} \)

Question. The arithmetic mean of the squares of the first n natural numbers is
(a) \( \frac{(n+1)}{6} \)
(b) \( \frac{(n+1)(2n+1)}{6} \)
(c) \( \frac{(n^2-1)}{6} \)
(d) \( n \)
Answer: (b) \( \frac{(n+1)(2n+1)}{6} \)

Question. The standard deviation of a variable x is \( \sigma \). The standard deviation of the variable \( \frac{ax + b}{c} \) where a, b, c are constants is ...
(a) \( \left( \frac{a}{c} \right) \sigma \)
(b) \( \left| \frac{a}{c} \right| \sigma \)
(c) \( \frac{a^2}{c^2} \sigma \)
(d) \( \left( \frac{2a}{c} \right) \sigma \)
Answer: (b) \( \left| \frac{a}{c} \right| \sigma \)

Question. If the mean of the set of numbers \( x_1, x_2, \dots, x_n \) is \( \overline{x} \), then the mean of the numbers \( x_i + 2i, 1 \leq i \leq n \) is
(a) \( \overline{x} + n + 1 \)
(b) \( \overline{x} + 2n \)
(c) \( \overline{x} + 2 \)
(d) \( \overline{x} + n \)
Answer: (a) \( \overline{x} + n + 1 \)

Question. If each observation of a raw data, whose variance is \( \sigma^2 \), is multiplied by \( \lambda \), then the variance of the new set is
(a) \( \sigma^2 \)
(b) \( \sigma^2 \lambda^2 \)
(c) \( \sigma^2 + \lambda \)
(d) \( \sigma^2 + \lambda^2 \)
Answer: (b) \( \sigma^2 \lambda^2 \)

Question. If a variable takes values 0, 1, 2, 3, ....... with frequencies proportional to \( e^{-\lambda}, e^{-\lambda}\lambda, \frac{e^{-\lambda}\lambda^2}{2!}, \frac{e^{-\lambda}\lambda^3}{3!}, \dots \) then the mean of the distribution is
(a) \( e^{-\lambda} \)
(b) \( \lambda \)
(c) \( e^{-\lambda}\lambda \)
(d) \( \left(\frac{1}{2}\right)e^{-\lambda}\lambda^2 \)
Answer: (b) \( \lambda \)

Question. A cyclist covers his first three miles at an average speed of 8 m.p.h. Another two miles at 3 m.p.h. and the last two miles at 2 m.p.h. The average speed for the entire journey is : (in m.p.h.)
(a) 3
(b) 2.4
(c) 3.8
(d) 3.43
Answer: (d) 3.43

Question. For overlapping classes 0-10, 10-20, 20-30, etc. Then the class mark of the class 0-10 is
(a) 0
(b) 10
(c) 5
(d) 6
Answer: (c) 5

Question. Which one of the following measures is the most suitable one of central location for computing intelligence of students?
(a) Mode
(b) A.M.
(c) G.M.
(d) Median
Answer: (d) Median

Question. The mean of 20 observations is 15. On checking it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is
(a) 15
(b) 15.15
(c) 16.15
(d) 17
Answer: (b) 15.15

Question. The mean weight of 9 items is 15. If one more item is added to the series the mean becomes 16. The value of 10th item is
(a) 35
(b) 30
(c) 25
(d) 20
Answer: (c) 25

Question. When 15 was subtracted from each of the seven observations the following number resulted : -3, 0, -2, 4, 6, 1, 1. The mean of the distribution is
(a) 14
(b) 15
(c) 16
(d) 17
Answer: (c) 16

Question. Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is.
(a) 48
(b) \( 82 \frac{1}{2} \)
(c) 80
(d) 50
Answer: (d) 50

Question. If the arithmetic and harmonic means of two numbers are 4.5 and 4 respectively, then one of the number is
(a) 5
(b) 6
(c) 7
(d) 4
Answer: (b) 6

Question. If the mode of a data is 18 and the mean is 24, then median is
(a) 18
(b) 24
(c) 21
(d) 22
Answer: (d) 22

Question. If the median of 21 observations is 40 and if the observations greater than the median are increased by 6 then the median of the new data will be
(a) 40
(b) 46
(c) \( 46 + \frac{40}{21} \)
(d) \( 46 - \frac{40}{21} \)
Answer: (a) 40

Question. Mode of the data 3, 2, 5, 2, 3, 5, 6, 6, 5, 3, 5, 2, 5 is
(a) 6
(b) 4
(c) 3
(d) 5
Answer: (d) 5

Question. Mode of the distribution
Marks: 4, 5, 6, 7, 8
No.of students: 3, 5, 10, 6, 1
(a) 6
(b) 10
(c) 8
(d) 4
Answer: (a) 6

Question. The range of the following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is
(a) 11
(b) 7
(c) 5.5
(d) 6
Answer: (b) 7

Question. The quartile deviation of daily wages (in Rs.) of 7 persons given below is 12, 7, 15, 10, 17, 17, 25 is
(a) 14.5
(b) 5
(c) 3.5
(d) 4.5
Answer: (c) 3.5

Question. If the standard deviation of 0, 1, 2, 3 ..... 9 is K, then the standard deviation of 10, 11, 12, 13 \dots 19 is
(a) K + 10
(b) K
(c) \( \sqrt{10} + \text{K} \)
(d) 10 K
Answer: (b) K

Question. The variance of the first n natural numbers is
(a) \( \frac{n^2 - 1}{12} \)
(b) \( \frac{n^2 - 1}{6} \)
(c) \( \frac{n^2 + 1}{6} \)
(d) \( \frac{n^2 + 1}{12} \)
Answer: (a) \( \frac{n^2 - 1}{12} \)

Question. The mean of four observations is 3. If the sum of the squares of these observations is 48 then their standard deviation is [EAMCET-2014]
(a) \( \sqrt{2} \)
(b) \( \sqrt{3} \)
(c) \( \sqrt{5} \)
(d) \( \sqrt{7} \)
Answer: (b) \( \sqrt{3} \)

Question. If \( x_1, x_2, \dots , x_n \) are n observations such that \( \sum_{i=1}^n x_i^2 = 400 \) and \( \sum_{i=1}^n x_i = 80 \) then the least value of n is [EAMCET-2014]
(a) 12
(b) 15
(c) 16
(d) 18
Answer: (c) 16

Question. The sum of 10 items is 12 and sum of their squares is 18, then standard deviation is
(a) \(-3/5\)
(b) 6/5
(c) 4/5
(d) 3/5
Answer: (d) 3/5

Question. The mean of two samples of sizes 200 and 300 were found to be 25, 10 respectively. Their standard deviations were 3 and 4 respectively. The variance of combined sample of size 500 is
(a) 64
(b) 65.2
(c) 67.2
(d) 64.2
Answer: (c) 67.2

Question. For the class intervals 0-5, 5-10, 10-15, etc. The length of the class is ......
(a) 5
(b) 10
(c) 0
(d) 6
Answer: (a) 5

Question. Which of the following is not a measure of dispersion?
(a) Variance
(b) Mean Deviation
(c) Mode
(d) Standard Deviation
Answer: (c) Mode

Question. Which of the following would you regard as discrete variable
(a) height
(b) weight
(c) time
(d) number of persons in family
Answer: (d) number of persons in family

Question. The average salary of male employees in a firm was Rs. 520 and that of females was Rs. 420. The mean salary of all the employees was Rs. 500. The percentage of male and female employees are
(a) 30, 70
(b) 80, 20
(c) 40, 60
(d) 50, 50
Answer: (b) 80, 20

Question. Mean of 10 numbers is 6. It was later observed that one number was misread as 9. When the correct mean was 7, then the correct value of that number is
(a) 19
(b) 20
(c) 8
(d) 10
Answer: (a) 19

Question. The median of the scores 25,28,20,8,10,15 is
(a) 17.5
(b) 16.5
(c) 20.2
(d) 13.5
Answer: (a) 17.5

Question. A data consists of two 2’s, four 4’s, six 6’s, three 8’s, and 10. Then the mode of data is
(a) 2
(b) 4
(c) 6
(d) 8
Answer: (c) 6

Question. In a moderately asymmetrical series, the values of arithmetic mean and mode are at 20.6 and 34.1 respectively. The value of the median is
(a) 25.1
(b) 28.0
(c) 23.4
(d) 35.3
Answer: (a) 25.1

Question. For a symmetric distribution \( Q_1=20 \), \( Q_3=40 \) the median of data is
(a) 20
(b) 30
(c) 40
(d) 10
Answer: (b) 30

Question. The standard deviation of the data given by
Variate (x) 0 1 2 3. . . . . n
Frequency (f) \( ^nC_0 \) \( ^nC_1 \) \( ^nC_2 \) \( ^nC_3 \) . . . . \( ^nC_n \)
(a) \( \sqrt{\frac{(n+1)}{2}} \)
(b) \( \sqrt{\frac{n}{2}} \)
(c) \( \frac{2^n}{n} \)
(d) \( \frac{\sqrt{n}}{2} \)
Answer: (d) \( \frac{\sqrt{n}}{2} \)

Question. Variance of the data 2, 4, 6, 8, 10 is
(a) 6
(b) 7
(c) 8
(d) 9
Answer: (c) 8

Question. The geometric mean of 10 observations on a certain variable was calculated as 16.2. It was later discovered that one of the observations was wrongly recorded as 12.9; infact it was 21.9. The correct geometric mean is
(a) \( \left( \frac{(16.2)^9 \times 21.9}{12.9} \right)^{1/10} \)
(b) \( \left( \frac{(16.2)^{10} \times 21.9}{12.9} \right)^{1/10} \)
(c) \( \left( \frac{(16.2)^{10} \times 12.9}{21.9} \right)^{1/10} \)
(d) \( \left( \frac{(16.2)^{11} \times 21.9}{12.9} \right)^{1/11} \)
Answer: (b) \( \left( \frac{(16.2)^{10} \times 21.9}{12.9} \right)^{1/10} \)

Question. The A.M. of the observations 1.3.5, 3.5.7, 5.7.9, ......., (2n-1)(2n+1)(2n+3) is \( (\forall n \in N) \)
(a) \( 2n^3 + 6n^2 + 7n - 2 \)
(b) \( n^3 + 8n^2 + 7n - 2 \)
(c) \( 2n^3 + 5n^2 + 6n - 1 \)
(d) \( 2n^3 + 8n^2 + 7n - 2 \)
Answer: (d) \( 2n^3 + 8n^2 + 7n - 2 \)

Question. The mean weight of 9 items is 15. If one more item is added to the series the mean becomes 16. The value of 10th item is
(a) 35
(b) 30
(c) 25
(d) 20
Answer: (c) 25