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. 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. If a variance of the following frequency distribution :**

**is 50, then x is equal to _____________.**

## Answer

4

**Question. The average marks of boys in 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) 80

(b) 60

(c) 40

(d) 20

## Answer

A

**Question. Let x _{1}, x_{2} , ………….. x_{n} be n observations such that ∑x_{i}^{2} = 400 and ∑x_{i} = 80. Then the possible value of n among the following is**

(a) 15

(b) 18

(c) 9

(d) 12

## Answer

B

**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

**Question. The outcome of each of 30 items was observed; 10 items gave an outcome 1/2 − d each, 10 items gave outcome 1/2 each and the remaining 10 items gave outcome 1/2 + d each. If the variance of this outcome data is 4/3 then |d| equals :**

(a) 2/3

(b) 2

(c) √5/2

(d) √2

## Answer

D

**Question. The mean of a set of 30 observations is 75. If each other observation is multiplied by a non- ero number λ and then each of them is decreased by 25, their mean remains the same. The λ 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. 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. If the variance of the terms in an increasing A.P., b _{1} , b_{2} , b_{3} , ….., b_{11} is 90, then the common difference of this A.P. is ___________.**

## Answer

3

**Question. A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is ₹ 54 and per day mean wage of all the workers is ₹ 60, then per day mean wage of the night shift workers (in ₹) is :**

(a) 69

(b) 66

(c) 74

(d) 75

## Answer

C

**Question. In a set of 2n distinct observations, each of the observations below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then the mean of the new set of observations:**

(a) increases by 1

(b) decreases by 1

(c) decreases by 2

(d) increases by 2

## Answer

A

**Question. Consider the data on x taking the values 0, 2, 4, 8, …, 2 ^{n} with frequencies ^{n}C_{0}, ^{n}C_{1}, ^{n}C_{2}, …, ^{n}C_{n} respectively. If the mean of this data is 728/2^{n}, then n is equal to ______.**

## Answer

6.00

**Question. The minimum value of 2 ^{sin x} + 2^{cos x} is :**

## 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. The frequency distribution of daily working expenditure of families in a locality is as follows:**

**If the mode of the distribution is ₹ 140, then the value of b is**

(a) 34

(b) 31

(c) 26

(d) 36

## Answer

D

**Question. The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is:**

(a) 10 : 3

(b) 4 : 9

(c) 5 : 8

(d) 6 : 7

## Answer

B

**Question. If mean and standard deviation of 5 observations x _{1}, x_{2}, x_{3}, x_{4}, x_{5} are 10 and 3, respectively, then the variance of 6 observations x_{1}, x_{2}, …, x_{5} and – 50 is equal to:**

(a) 509.5

(b) 586.5

(c) 582.5

(d) 507.5

## Answer

D

**Question. If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately**

(a) 22.0

(b) 20.5

(c) 25.5

(d) 24.0

## Answer

D

**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. If the data x _{1}, x_{2}, ……, x_{10} 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 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) x^{2} -10x +18 = 0

(b) 2x^{2} – 20x +19 = 0

(c) x^{2} – 10x +19 = 0

(d) x^{2} – 20x +18 = 0

## Answer

C

**Question. Let x _{1} , x_{2},…., x_{n} be n observations, and let x̅ be their arithmetic mean and σ^{2} be the variance.**

**Statement-1**: Variance of 2x

_{1}, 2x

_{2}, …, 2x

_{n}is 4σ

^{2}.

**Statement-2 :**Arithmetic mean 2x

_{1}, 2x

_{2}, …, 2x

_{n}is 4 x̅ .

(a) Statement-1 is false, Statement-2 is true.

(b) Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.

(c) Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.

(d) Statement-1 is true, statement-2 is false.

## Answer

D

**Question. Statement 1:** The variance of first n odd natural numbers is (n^{2}−1)/3**Statement 2:** The sum of first n odd natural number is n^{2} and the sum of square of first n odd natural numbers is (n(4n^{2}+1)) / 3

(a) Statement 1 is true, Statement 2 is false.

(b) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

(c) Statement 1 is false, Statement 2 is true.

(d) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

## Answer

A

**Question. For the frequency distribution :**

**where 0 < x _{1} < x_{2} < x_{3} < … < x_{15} = 10 and**

**the standard deviation cannot be :**

(a) 4

(b) 1

(c) 6

(d) 2

## Answer

C

**Question. Let x _{1}(1 ≤ i ≤ 10) be ten observations of a random variable X. If**

**where 0 ≠ p ∈ R, then the standard deviation of these observations is :**

(a) √(3/5)

(b) 4/5

(c) 9/10

(d) 7/10

## Answer

C

**Question. **

**then the standard deviation of the 9 items x _{1}, x_{2}, …, x_{9} is :**

(a) 4

(b) 2

(c) 3

(d) 9

## Answer

B

**Question. The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :**

(a) 8.25

(b) 8.50

(c) 8.00

(d) 9.00

## Answer

D

**Question. Let the observations x _{i}(1 ≤ i ≤ 10) satisfy the equations,**

**If μ and λ are the mean and the variance of the observations, x _{1} – 3, x_{2} – 3, …, x_{10} – 3, then the ordered pair (μ, λ) is equal to:**

(a) (3, 3)

(b) (6, 3)

(c) (6, 6)

(d) (3, 6)

## Answer

A

**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. A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standarion deviation of 2 gm. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 gm. The correct mean and standard deviation (in gm) of fishes are respectively :**

(a) 32, 2

(b) 32, 4

(c) 28, 2

(d) 28, 4

## Answer

A

**Question. If the mean deviation about the median of the numbers a, 2a,…….,50a is 50, then | a | equals**

(a) 3

(b) 4

(c) 5

(d) 2

## Answer

B

**Question. If both the mean and the standard deviation of 50 observations x _{1}, x_{2}, ….. , x_{50} are equal to 16, then the mean of (x_{1} – 4)^{2}, (x_{2} – 4)^{2}, …, (x_{50} – 4)^{2} is :**

(a) 400

(b) 380

(c) 525

(d) 480

## Answer

A

**Question. If for some x ∈ R, the frequency distribution of the marks obtained by 20 students in a test is :**

**then the mean of the marks is :**

(a) 3.2

(b) 3.0

(c) 2.5

(d) 2.8

## Answer

D

**Question. The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then y/x is equal to:**

(a) 9/4

(b) 7/2

(c) 8/3

(d) 7/3

## Answer

D

**Question. If the standard deviation of the numbers –1, 0, 1, k is √5 where k > 0, then k is equal to:**

(a) 2√6

(b) 2√(10/3)

(c) 4√(5/3)

(d) √6

## Answer

A

**Question. The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6; then the mean deviation from the mean of the data is :**

(a) 2.5

(b) 2.6

(c) 2.8

(d) 2.4

## Answer

C

**Question. If the mean deviation of the numbers 1, 1 + d, …, 1 + 100d from their mean is 255, then a value of d is :**

(a) 10.1

(b) 5.05

(c) 20.2

(d) 10

## Answer

A

**Question. Suppose a population A has 100 observations 101, 102, …………., 200 and another population B has 100 obsevrations 151, 152, ……………. 250. If V _{A} and V_{B} represent the variances of the two populations, respectively then V_{A}/V_{B} is**

(a) 1

(b) 9/4

(c) 4/9

(d) 2/3

## Answer

A

**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. 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. A data consists of n observations:**

**then the standard deviation of this data is:**

(a) 2

(b) √5

(c) 5

(d) √7

## Answer

B

**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. Statement-1 :** The variance of first n even natural numbers is (n^{2}-1)/4**Statement-2 :** 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

(a) Statement-1 is true, Statement-2 is true. Statement-2 is not a correct explanation for Statement-1.

(b) Statement-1 is true, Statement-2 is false.

(c) Statement-1 is false, Statement-2 is true.

(d) Statement-1 is true, Statement-2 is true. Statement-2 is a correct explanation for Statement-1.

## Answer

C

**Question. 5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is:**

(a) 16

(b) 22

(c) 20

(d) 18

## Answer

C

**Question. The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively.****If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is?**

(a) 0

(b) 4

(c) 2

(d) 1

## Answer

C

**Question. Consider the following statements :**

(A) Mode can be computed from histogram

(B) Median is not independent of change of scale

(C) Variance is independent of change of origin and scale.**Which of these is / are correct ?**

(a) (A), (B) and (C)

(b) Only (B)

(c) Only (A) and (B)

(d) Only (A)

## Answer

C

**Question. In an experiment with 15 observations on x, the following results were available:****∑x ^{2} = 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**

(a) 8.33

(b) 78.00

(c) 188.66

(d) 177.33

## Answer

B

**Question. If the mean of the data : 7, 8, 9, 7, 8, 7, l, 8 is 8, then the variance of this data is**

(a) 9/8

(b) 2

(c) 7/8

(d) 1

## Answer

D

**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. 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 standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?**

(a) 3a^{2} – 34a + 91 = 0

(b) 3a^{2} – 23a + 44 = 0

(c) 3a^{2} – 26a + 55 = 0

(d) 3a^{2} – 32a + 84 = 0

## Answer

D

**Question. The variance of first 50 even natural numbers is**

(a) 437

(b) 437/4

(c) 833/4

(d) 833

## Answer

D

**Question. The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :**

(a) 25

(b) 30

(c) 35

(d) 40

## Answer

C

**Question. The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is:**

(a) 15.8

(b) 14.0

(c) 16.8

(d) 16.0

## 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. In a set of 2n observations, half of them are equal to ‘a’ and the remaining half are equal to ‘ –a’. If the standard deviation of all the observations is 2 ; then the value of | α | is :**

(a) 2

(b) √2

(c) 4

(d) 2√2

## Answer

A

**Question. The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set**

(a) remains the same as that of the original set

(b) is increased by 2

(c) is decreased by 2

(d) is two times the original median.

## Answer

A

**Question. In a class of 100 students there are 70 boys whose average marks in a sub ect are 75. If the average marks of the complete class is 72, then what is the average of the girls?**

(a) 73

(b) 65

(c) 68

(d) 74

## Answer

B

**Question. Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10 and one is missing then the variance of all the five observations is :**

(a) 4

(b) 6

(c) 8

(d) 2

## Answer

D

**Question. If the mean of 4, 7, 2, 8, 6 and a is 7, then the mean deviation from the median of these observations is**

(a) 8

(b) 5

(c) 1

(d) 3

## Answer

D

**Question. For two data sets, each of si e 5, the variances 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) 11/2

(b) 6

(c) 13/2

(d) 5/2

## Answer

A

**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

## Answer

D

**Question. The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal to:**

(a) –5

(b) 10

(c) –20

(d) –10

## 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

A

**Question. Let x̅ , M and σ ^{2} be respectively the mean, mode and variance of n observations x_{1}, x_{2}, …., x_{n} and d_{i} = – x_{i} – a , i = 1, 2, …., n, where a is any number.**

**Statement I:**Variance of d

_{1}, d

_{2},… d

_{n}is σ

^{2}.

**Statement II:**Mean and mode of d

_{1}, d

_{2}, …. d

_{n}are – x̅ – a and – M – a, respectively.

(a) Statement I and Statement II are both false

(b) Statement I and Statement II are both true

(c) Statement I is true and Statement II is false

(d) Statement I is false and Statement II is true

## Answer

B

**Question. Let X̅ and M.D. be the mean and the mean deviation about X̅ 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) X̅,M.D.

(b) X̅ + 5,M.D.

(c) X̅,M.D.+ 5

(d) X̅ + 5,M.D.+ 5

## Answer

B

**Question. **

**then the standard deviation of n observations x _{1}, x_{2}, …, x_{n} is :**

(a) a – 1

(b) n√(a -1)

(c) √(n(a -1))

(d) √(a -1)

## Answer

D

**Question. The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is :**

(a) 1

(b) 4

(c) 2

(d) 3

## Answer

C

**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 mean of a data set consisting of 20 observations is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be :**

(a) 41

(b) 49

(c) 40.5

(d) 42.5

## Answer

A