MCQs For NCERT Class 11 Mathematics Chapter 15 Statistics

Please refer to the MCQ Questions for Class 11 Statistics Maths Chapter 15 with Answers. The following Statistics Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Statistics with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

Statistics Class 11 MCQ Questions with Answers

See below Statistics Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. Find the mean and standard deviation for the following data :

(a) mean = 6.59, S.D = 19
(b) mean = 8, S.D = 19
(c) mean = 19, S.D = 6.59
(d) mean = 19, S.D = 6

Question. If the mean of n observations 1², 2², 3²,…., n² is 46n/11 ,then n is equal to
(a) 11
(b) 12
(c) 23
(d) 22

Question. Which of the following is/are used for the measures of dispersion?
(a) Range
(b) Quartile deviation
(c) Standard deviation
(d) All of these

Question. Consider the following frequency distribution

where, A is a positive integer and has variance 160. Then the value of A is.
(a) 5
(b) 6
(c) 7
(d) 8

Question. Consider the first 10 positive integers. If we multiply each number by (– 1) and then add 1 to each number, the variance of the numbers so obtained is
(a) 8.25
(b) 6.5
(c) 3.87
(d) 2.87

Question. The coefficient of variation from the given data

(a) 50
(b) 51.9
(c) 48
(d) 51.8

Question. The range of set of observations 2, 3, 5, 9, 8, 7, 6,5, 7, 4, 3 is
(a) 6
(b) 7
(c) 4
(d) 5

Question. Variance of the numbers 3, 7, 10,18, 22 is equal to
(a) 12
(b) 6.4
(c) 49.2
(d) 49.2

Question. The reciprocal of the mean of the reciprocals of nobservation is the :
(a) geometric mean
(b) median
(c) harmonic mean
(d) average

Question. If X and Y are two variates connected by the relation Y = aX + b/c and Var (X) = σ², then write the expression for the standard deviation of Y.

Question. The variance of the data 2, 4, 6, 8, 10 is
(a) 8
(b) 7
(c) 6
(d) None of these

Question. The mean of n items is x̄. If the first item is increased by 1, second by 2 and so on, the new mean is :

Question. Let x₁, x₂, x₃, x₄ and x₅ be the observations with mean m and standard deviations. Then, standard deviation of the observations kx₁, kx₂, kx₃, kx₄ and kx₅ is
(a) k + 5
(b) π / k
(c) ks
(d) s

Question. The mean deviation from the median of the following data is

(a) 14
(b) 10
(c) 5
(d) 7

Question. The method used in Statistics to find a representative value for the given data is called
(a) measure of skewness
(b) measure of central tendency
(c) measure of dispersion
(d) None of the above

Question. The coefficient of variation is computed by:
(a) mean /standard deviation
(b) standard deviation / mean
(c) mean / standard deviation ×100
(d) standard deviation /mean ×100

Question. The mean deviation from the mean of the set of observations – 1, 0 and 4 is
(a) 3
(b) 1
(c) – 2
(d) 2

Question. 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

Question. In computing a measure of the central tendency for any set of 51 numbers, which one of the following measures is welldefined but uses only very few of the numbers of the set?
(a) Arithmetic mean
(b) Geometric mean
(c) Median
(d) Mode

Question. Number which is mean of the squares of deviations from mean, is called …… .
(a) standard deviation
(b) variance
(c) median
(d) None of these

Question. Consider the following data.
36, 72, 46, 42, 60, 45, 53, 46, 51, 49
Then the mean deviation about the median for the data is
(a) 6
(b) 8
(c) 7
(d) None of these

Question. The mean of a set of 20 observation is 19.3. The mean is reduced by 0.5 when a new observation is added to the set. The new observation is
(a) 19.8
(b) 8.8
(c) 9.5
(d) 30.8

Question. Consider the following data
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
If 1 is added to each number, then variance of the numbers so obtained is
(a) 6.5
(b) 2.87
(c) 3.87
(d) 8.25

Question. All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?
(a) mean
(b) median
(c) mode
(d) variance

Question. Find the mean deviation about the mean for the data.

(a) 6
(b) 7.3
(c) 8
(d) 6.32

Question. The mean of 13 observations is 14. If the mean of the first 7 observations is 12 and that of the last 7 observations is 16, what is the value of the 7th observation ?
(a) 12
(b) 13
(c) 14
(d) 15

Question. If n = 10, x̄ = 12 and ∑x_i² =1530 , then the coefficient of variation is
(a) 35%
(b) 42%
(c) 30%
(d) 25%

Question. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b ?
(a) a = 0, b = 7
(b) a = 5, b = 2
(c) a = 1, b = 6
(d) a = 3, b = 4

Question. Match the terms given in column-I with the terms given in column-II and choose the correct option from the codes given below.

Codes
A B C D
(a) 3 4 1 2
(b) 4 3 2 1
(c) 3 4 2 1
(d) 4 3 1 2

Question. The observation which occur most frequently is known as :
(a) mode
(b) median
(c) weighted mean
(d) mean

Question. The value which represents the measure of central tendency, is/are
(a) mean
(b) median
(c) mode
(d) All of these

Question. The variance of n observations x₁, x₂, …., x_n is given by

Question. The measure of dispersion is:
(a) mean deviation
(b) standard deviation
(c) quartile deviation
(d) all (a) (b) and (c)

Question. The mean and variance for first n natural numbers are respectively
(a) mean = n + 1/2 , variance = n² − 1/12
(b) mean = n − 1/2 , variance = n² + 1/12
(c) mean = n² − 1/12 , variance = n + 1/2
(d) mean = n² + 1/2 , variance = n − 1/2

Question. The variance of 20 observations is 5. If each observation is multiplied by 2, then the new variance of the resulting observation is
(a) 2³ × 5
(b) 2² × 5
(c) 2 × 5
(d) 2⁴ × 5

Question. The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b ?
(a) a = 0, b = 7
(b) a = 5, b = 2
(c) a = 1, b = 6
(d) a = 3, b = 4

Question. Standard deviation for first 10 natural numbers is
(a) 5.5
(b) 3.87
(c) 2.97
(d) 2.87

Question. Given N = 10, ∑x = 60 and ∑x² = 1000. The standard deviation is
(a) 6
(b) 7
(c) 8
(d) 9

Question. The median of 18, 35, 10, 42, 21 is
(a) 20
(b) 19
(c) 21
(d) 22

Question. The mean deviation from the mean of the following data :

(a) 10
(b) 10.22
(c) 9.86
(d) 9.44

Question. The mean deviation from the mean for the set of observations –1, 0, 4 is
(a) 3
(b) 2
(c) 1
(d) None of these

Question. Coefficient of variation of two distribution are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic means?
(a) 35, 22.85
(b) 22.85, 35.28
(c) 36, 22.85
(d) 35.28, 23.85

Question. We can grouped data into ……. ways.
(a) three
(b) four
(c) two
(d) None of these

Question. Coefficient of variation of two distributions are 50 and 60 and their arithmetic means are 30 and 25, respectively. Then, difference of their standard deviations is
(a) 0
(b) 1
(c) 1.5
(d) 2.5

Question. Coefficient of variation of two distribution are 50% and 60% and their standard deviation are 10 and 15, respectively. Then, difference of their arithmetic means is
(a) 3
(b) 4
(c) 5
(d) 6

Question. While dividing each entry in a data by a non-zero number a, the arithmetic mean of the new data:
(a) is multiplied by a
(b) does not change
(c) is divided by a
(d) is diminished by a

ASSERTION – REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question. Assertion : The mean deviation of the data 2, 9, 9, 3, 6, 9, 4 from the mean is 2.57
Reason : For individual observation, 
Mean deviation (X) = ∑ l x_i − x̄ l/n

Question. Let x₁, x₂, …., x_n be n observations, and let x̄ be their arithmetic mean and σ² be the variance.
Assertion : Variance of 2x₁,2x₂, …., 2x_n is 4 σ².
Reason : Arithmetic mean of 2x₁,2x₂, …., 2x_n is 4x .

Question. Assertion : The range is the difference between two extreme observations of the distribution.
Reason : The variance of a variate X is the arithmetic mean of the squares of all deviations of X from the arithmetic mean of the observations.

Question. Assertion : Mean of deviations = Product of deviations/No. of observations
Reason : To find the dispersion of values of x from mean x̄ , we take absolute measure of dispersion.

Question. Assertion : Sum of absolute values of Mean of deviations = Deviations/Number of observations
Reason : Sum of the deviations from mean (x̄) is 1.