CBSE Class 11 Mathematics Statistics Worksheet Set 01

Question. The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is :
(a) 45
(b) 49
(c) 48
(d) 40
Answer : C

Question. The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is:
(a) 3.99
(b) 4.01
(c) 4.02
(d) 3.98
Answer : C

Question. If the mean and the standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation :
(a) 2 x² -10x + 18 = 0
(b) 2x² - 20x + 19 = 0
(c) x² -10x + 19 = 0
(d) x² - 20x + 18 = 0
Answer : C

Question. The mean of a set of 30 observations is 75. If each other observation is multiplied by a non- ero number l and then each of them is decreased by 25, their mean remains the same. The l is equal to
(a) 10/3
(b) 4/3
(c) 1/3
(d) 2/3
Answer : B

Question. Let the sum of the first three terms of an A. P, be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :
(a) 28
(b) 26.5
(c) 29.5
(d) 31
Answer : C

Question. The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :
(a) 9
(b) 5
(c) 3
(d) 7
Answer : D

Question. Let X = {x ∈ N : 1 ≤ x ≤17} and Y = {a x + b : x ∈ X and a, b ∈ R, a > 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to :
(a) 7
(b) –7
(c) –27
(d) 9
Answer : B

Question. A student scores the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is : 
(a) 10/√3
(b) 100/√3
(c) 10/3
(d) 100/√3
Answer : A

Question. If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :
(a) 30
(b) 51
(c) 50
(d) 31
Answer : D

Question. If the data x₁, x₂, ……, x₁₀ is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :
(a) 2√2
(b) 2
(c) 4
(d) √2
Answer : B

Question. If both the mean and the standard deviation of 50 observations x₁, x₂, ….. , x₅₀ are equal to 16, then the mean of (x₁ – 4)², (x₂ – 4)², …, (x₅₀ – 4)² is :
(a) 400
(b) 380
(c) 525
(d) 480
Answer : A

Question. The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is : 
(a) 7
(b) 5
(c) 1
(d) 3
Answer : A

Fill in The Blanks

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. If the variance of the terms in an increasing A.P., b₁ , b₂ , b₃ , ....., b₁₁ is 90, then the common difference of this A.P. is ___________.
Answer : (3)

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

Question. Consider the data on x taking the values 0, 2, 4, 8, ..., 2n with frequencies ⁿC₀, ⁿC₁, ⁿC₂, ..., ⁿC_n respectively. If the mean of this data is 728/2ⁿ, then n is equal to ______.
Answer : (6.00)

Case Based MCQs

Consider the data
Class         Frequency
0-10                6
10-20              7
20-30            15
30-40            16
40-50             4
50-60             2

Based above information answer the following questions

Question. Total frequency of the given data is
(a) 10
(b) 20
(c) 50
(d) 60
Answer : C

Question. Median of the given data is
(a) 28
(b) 20
(c) 18
(d) 8
Answer : A

Question. Mean deviation about median is
(a) 10.16
(b) 15
(c) 9.16
(d) 8.5
Answer : A

For a group of 200 candidates, the mean and the standard deviation of scores were found to be 40 and 15, respectively. Later on it was discovered that the scores of 43 and 35 were misread as 34 and 53, respectively.

Answer the following questions on the basis of above information.

Question. Find the sum of correct scores.
(a) 7991
(b) 8000
(c) 8550
(d) 6572
Answer : A

Question. Find the correct mean.
(a) 42.924
(b) 39.955
(c) 38.423
(d) 41.621
Answer : B

Question. Find the correct variance.
(a) 280.3
(b) 235.6
(c) 224.143
(d) 226.521
Answer : C

Question. Find the correct standard deviation.
(a) 14.971
(b) 11.321
(c) 16.441
(d) 12.82
Answer : A

Please click on below link to download CBSE Class 11 Mathematics Statistics Worksheet Set A