VBQs Statistics Class 11 Mathematics with solutions has been provided below for standard students. We have provided chapter wise VBQ for Class 11 Mathematics with solutions. The following Statistics Class 11 Mathematics value based questions with answers will come in your exams. Students should understand the concepts and learn the solved cased based VBQs provided below. This will help you to get better marks in class 11 examinations.

**Statistics VBQs Class 11 Mathematics**

**Question: Coefficient of skew ness for the values Median = 18 8. , Q _{1} = 14 6. , Q_{3} = 252. is**

(a) 0.2

(b) 0.5

(c) 0.7

(d) None of these

## Answer

A

**Question: Which of the following is a correct statement?**

(a) The sum of the deviations from arithmetic mean is zero

(b) Computation of arithmetic mean is based on all observations

(c) It gives no importance to extreme values

(d) None of the above

## Answer

(A,B)

**Question: The variable x takes two values x1 andx2 with frequencies f1 andf2, , respectively. If σ denotes the standard deviation of x, then**

## Answer

(A,B)

** Let us consider the series x2,x2,…,x n whose mean is x and variance is σ ^{2}.**

**On the basis of above information, answer the following questions.**

**Question: If 5 is added in each observation, then the new variance is**

(a) σ^{2}

(b) σ^{2} + 5

(c) σ^{2}-5

(d) None of these

## Answer

A

**Question: If xi is replaced by xi’, then new mean is**

(a) x̅ – xi + xi’

(b)(n-1) x̅ + x_{i}‘

(c) n x̅ – xi + xi /n

(d) None of these

## Answer

C

**Assertion and Reason**** Each of these questions contains two**.**statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.**

(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.

(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.

(c) Statement I is true; Statement II is false.

(d) Statement I is false; Statement II is true.

**Question: The algebraic sum of deviation from their mean is defined as **

**Statement I** The algebraic sum of the deviations of 20 observations measured from 30 is 2. The mean value of the observations is 30.**Statement II** The sum of deviation from their mean is zero.

## Answer

D

**Question: Suppose two groups of scores A and B are such that A = (+, x+2, x+4) and B= (x-2, x+2, x+6)****Statement I** Group B has more variability than group A.**Statement II** The value of mean for group B is more than that of group A.

## Answer

C

**Question: Standard deviation is not depend on change of origin.****Statement I** The standard deviation of variable ax+ b/c

**Statement II** The standard deviation of a linear equation is σ x |coefficient of x|.

## Answer

A

**Question: If n is a natural number, then ****Statement I** The mean of the squares of first n natural number is (n+1)(2n+1)/6.**Statement II** ∑n = n(n+1)/2

## Answer

B

**Question: Statement I** If μ is the mean of a distribution, then ∑fi (yi-μ ) is equal to 0.**Statement II** The mean of the square of first n natural numbers is 1/6 n(2n+1).

## Answer

C

**Question: Statement I** The variance of first n natural numbers is n2-1/12..**Statement II** The sum of first n natural numbers is n(n +1)/2 and the sum of squares of first n natural numbers is n(n+1) (2n+1/6

## Answer

A

**Question: If the mean deviations about the median of the numbers a, 2a,…,5a is 50, then |a| is equal to**

(a) 3

(b) 4

(c) 5

(d) 2

## Answer

B

**Question: If the mean deviation of number 1,1+d,1+2d,…1 +10d from their mean is 255,then the d is equal to**

(a) 10.0

(b) 20.0

(c) 10.1

(d) 20.2

## Answer

C

**Question: For two data sets, each of size 5, the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is **

(a) 5/2

(b) 11/2

(c) 6

(d) 13/2

## Answer

B

**Question: The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is**

(a) 40%

(b) 20%

(c) 80%

(d) 60%

## Answer

C

**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 b and ? **

(a) a =3, b=4

(b) a = 0, b=7

(c) a = 5, b=2

(d) a = 1, b= 6

## Answer

A

**Question: Median of ^{2n}Co,^{2n}C1,^{2n}C_{2,}^{2n}C_{3,…,2nCn} (where, n is even) is**

(a) 2nCn/2

(b) 2nCn+1/2

(c) 2nCn-1/2

(d) None of these

## Answer

A

**Question: If a variable takes the discrete values α + 4 , α -7/2,α-5/2,α-3, α-2,α+1/2, α+5(α>0), 5/2, α-3, α-1/2 ,then the median is**

(a) α – 5/4

(b) α – 1/2

(c) α – 2

(d) α +5/4

## Answer

A

**Question: If the mode of the data is 18 and the mean is 24, then median is**

(a) 18

(b) 24

(c) 22

(d) 21

## Answer

A

**Question: If in a moderately asymmetrical distribution mode and mean of the data are 6l and 9l respectively, then median is**

(a) 8λ

(b) 7λ

(c) 6λ

(d) 5λ

## Answer

A

**Question: If the median of 21 observations is 40 and if the observations greater than the median are increased by 5, then the median of the new data will be**

(a) 40

(b) 45

(c) 4+50/21

(d) 45-50/21

## Answer

A

**Question: In a moderately skewed distribution the values of mean and median are 5 and 6, respectively. The value of mode in such a situation is approximately equal to**

(a) 8

(b) 11

(c) 16

(d) None of these

## Answer

A

**Question: If the sum of 11 consecutive natural numbers is 2761, then the middle number is**

(a) 249

(b) 250

(c) 251

(d) 252

## Answer

C

**Question: Consider the following statements I. The values of median and mode can be determined graphically.****II. Mean, median and mode have the same unit.****III. Range is the best measure of dispersion.****Which of these is/are correct?**

(a) Only I

(b) Only II

(c) Both II and III

(d) None of these

## Answer

A

**Question: The quartile deviation for the following data is**

(a) 0

(b) 1/4

(c) 1/2

(d) 1

## Answer

D

**Question: When tested, the lives (in hours) of 5 bulbs were noted as follows 1357, 1090, 1666, 1494, 1623 The mean deviations (in hours) from their mean is**

(a) 178

(b) 179

(c) 220

(d) 356

## Answer

A

**Question: The quartile deviation of daily wages (in R.s.) of 7 persons given below 12, 7, 15, 10, 17, 19 and 25 is**

(a) 14.5

(b) 5

(c) 9

(d) 4.5

## Answer

D

**Question: If two variables x y and are such that 2y+5=3x and Quartile Deviation (QD) of x is 8, then (QD) of y is**

(a) 2

(b) 8

(c) 4

(d) None of these

## Answer

D

**Question: The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is **

(a) 2

(b) 2.57

(c) 3

(d) 3.75

## Answer

B

**Question: For a series the value of mean deviation is 15, the most likely value of its quartile deviation is**

(a) 12.5

(b) 11.6

(c) 13

(d) 9.7

## Answer

A

**Question: Following are the marks obtained by 9 students in a Mathematics test 50, 69, 20, 33, 53, 39, 40, 65, 59 The mean deviation from the median is**

(a) 9

(b) 10.5

(c) 12.67

(d) 14.76

## Answer

C

**Question: Find the quartile deviation of the following distribution**

(a) 8.20

(b) 8.25

(c) 8.30

(d) None of these

## Answer

B

**Question: Find the mean deviation from the median of the following data **

(a) 7.08

(b) 7

(c) 7.1

(d) 7.05

## Answer

B

**Question: Find the mean deviation about the mean of the set of first n natural numbers when n is an odd number**.

(a) n^{2}+1/4n

(b) n^{2}-1/4n

(c) n^{2}-3/5n

(d) None of these

## Answer

B

**Question: The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is **

(a) 50000

(b) 250000

(c) 252500

(d) 255000

## Answer

C

**Question: Let a, b, c, d e and e be the observations with mean m and standard deviation S. The standard deviation of the observations a+ k, b+ k c+ k ,d +k, e+ k is**

(a) S

(b) k S

(c) S +k

(d) S/k

## Answer

A

**Question: The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is **

(a) √52/7

(b) 52/7

(c) 6

(d) 6

## Answer

A

**Question: The SD of 15 items is 6 and if each item is decreases by 1, then standard deviation will be**

(a) 5

(b) 7

(c) 91/15

(d) 6

## Answer

D

**Question: If x̅ is the arithmetic mean of n independent variates x _{1},x_{2},x_{3},…,x_{n} each of the standard deviation s, then variance (x̅ ) is**

(a) σ

^{2}/n

(b) n σ

^{2}

(c) (n+1 )σ

^{2}/3

(d) None of these

## Answer

A

**Question: If SD of X is S, then SD of the variable μ = aX+ b/c, where a, b and c are constants, is**

## Answer

B

**Question: Let x _{1},x_{2},x_{3},x_{4} and x_{5} and be the observations with mean m and standard deviation S. The standard deviation of the observations kx_{1}, kx_{2}, kx_{3}, kx_{4 } and is kx_{5} is**

(a) k+5

(b) S/k

(c) k S

(d) S

## Answer

C

**Question: The variance of the first n natural numbers is**

(a) (n^{2}-1/12)

(b) n (n^{2}-1/12)

(c) (n^{2}+1/12)

(d) n(n^{2} +1)/12

## Answer

A

**Question: Standard deviations for first 10 natural numbers is**

(a) 5.5

(b) 3.87

(c) 2.97

(d) 2.87

## Answer

D

**Question: Let x _{1},x_{2},..,x_{n} be n observations. Let w_{i} = l+_{i} +k for i=1,2,…,n, n = 1 2, , …, , where l and k are constants. If the mean of x_{i}‘s is 48 and their standard deviation is 12, the mean of w_{ i} ’s is 55 and standard deviation of w _{i }’s is 15, the values of l k and should be**

(a) l = 1.25 ,k = -5

(b) l = – 1.25, k = 5

(c) l = 2.5, k = -5

(d) l = 2.5 k = 5

## Answer

A

**Question: The following information relates to a sample of size 60 : ∑x2 = 18000, ∑x= 960. ****The variance is**

(a) 6.63

(b) 16

(c) 22

(d) 44

## Answer

D

**Question: The mean and variance of n values of a variable x are 0 and σ2 , respectively. If the variable y =x ^{2} , then mean of y is**

(a) σ

(b) σ

^{2}

(c) 1

(d) None of these

## Answer

B

**Question: Coefficient of variation of two distributions are 50 and 60 and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is**

(a) 0

(b) 1

(c) 1.5

(d) 2.5

## Answer

A

**Question: Consider the numbers 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

## Answer

D