CBSE Class 11 Mathematics HOTs Statistics

Question. The weighted mean of first n natural numbers whose weights are equal to the number of selections out of n natural numbers of corresponding numbers is
(a) n.2^n-1/2ⁿ-1
(b) 3n (n+1)/2 (2n+1)
(c) (n+1) (2n+1) / 6
(d) n (n+1)/2
Answer : A

Question. If M. D. is 12, the value of S.D. will be
(a) 15
(b) 12
(c) 24
(d) None of these
Answer : A

Question. If the median and the range of four numbers {x, y, 2x + y, x – y}, where 0 < y < x < 2y, are 10 and 28 respectively, then the mean of the numbers is :
(a) 18
(b) 10
(c) 5
(d) 14
Answer : D

Question. The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 - 30 and the number of observations less than 20 is 45, then the frequency of median class is
(a) 10
(b) 20
(c) 15
(d) 12
Answer : A

Question. If the mean deviation of the numbers 1, 1 + d, 1 + 2d, .... 1 + 100d from their mean is 255, then d is equal to :
(a) 20.0
(b) 10.1
(c) 20.2
(d) 10.0
Answer : B

Question. Let X and M.D. be the mean and the mean deviation about X of n observations x_i, i = 1, 2, ........, n. If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are :
(a) X, M.D.
(b) X + 5, M.D.
(c) X, M.D.+ 5
(d) X + 5, M.D.+ 5
Answer : B

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
Answer : D

Question. The mean of six numbers is 30. If one number is excluded, the mean of the remaining numbers is 29. The excluded number is
(a) 29
(b) 30
(c) 35
(d) 45
Answer : C

Question. The mean of n items is X . If the first item is increased by 1, second by 2 and so on, the new mean is :
(a) X¯ + x/2
(b) X¯+ x
(c) X¯ + n+1/2 
(d) none of these
Answer : C

Question. In a series of 2 n observations, half of them equal a and remaining half equal –a. If the standard deviation of the observations is 2, then |a| equals
(a)√2/n
(b) √2
(c) 2
(d) 1/n
Answer : C

Question. The A.M. of n observations is M. If the sum of n – 4 observation is a, then the mean of remaining 4 observation is
(a) nM–a/4
(b) nM+a/2
(c) nM–a/2
(d) nM + a
Answer : A

Question. Suppose values taken by a variable x are such that a ≤ x_i ≤ b, where xi denotes the value of x in i^th case for i = 1, 2, ... n. Then
(a) a ≤ Var(x) ≤ b
(b) a² ≤ Var(x) ≤ b²
(c) a²/4 ≤ Var(x)
(d) (b – a)² ≥ Var(x)
Answer : D

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
Answer : A

Question. The mean income of a group of persons is ₹ 400. Another group of persons has mean income ₹ 480. If the mean income of all the persons in the two groups together is ₹ 430, then ratio of the number of persons in the groups is 
(a) n₁/n₂ = 5/3
(b) n₁/n₂ = 2/5
(c) n₁/n₂ = 7/4
(d) None of these
Answer : A

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

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
Answer : B

Numeric Value Answer

Question. Variance of the data 2, 4, 5, 6, 8, 17 is 23.33. 
Then, variance of 4, 8, 10, 12, 16, 34 will be
Answer : 93.32

Question. In an experiment with 15 observations on x, the following results were available: ∑x² = 2830, ∑x = 170 One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is
Answer : 78

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
Answer : 8.25

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
Answer : 0

Question. The mean of 5 observation is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, then difference of the other two observations is
Answer : 5

Question. If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m + n is equal to _______.
Answer : 18

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
Answer : 5

Question. If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x × y is equal to ____.
Answer : 52