##### Class 10^{th} Mathematics Tamilnadu Board Solution

**Exercise 11.1**- 59, 46, 30, 23, 27, 40, 52, 35, 29 Find the range and coefficient of range of…
- 41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5 Find the range and coefficient…
- The smallest value of a collection of data is 12 and the range is 59. Find the…
- The largest of 50 measurements is 3.84 kg. If the range is 0.46 kg, find the…
- The standard deviation of 20 observations is √5. If each observation is…
- Calculate the standard deviation of the first 13 natural numbers.…
- 10, 20, 15, 8, 3, 4 Calculate the standard deviation of the following data.…
- 38, 40, 34 ,31, 28, 26, 34 Calculate the standard deviation of the following…
- |c|c|c|c|c|c| x&3&8&13&18&23 y&7&10&15&10&8 Calculate the standard deviation of…
- The number of books bought at a book fair by 200 students from a school are…
- Calculate the variance of the following data |c|c|c|c|c|c|c|c|c|
- The time (in seconds) taken by a group of people to walk across a pedestrian…
- A group of 45 house owners contributed money towards green environment of…
- Find the variance of the following distribution. |c|c|c|c|c|c|c|c|…
- Mean of 100 items is 48 and their standard deviation is 10. Find the sum of…
- The mean and standard deviation of 20 items are found to be 10 and 2…
- If n = 10 , bar x = 12 and sum x^2 = 1530 , then calculate the coefficient of…
- Calculate the coefficient of variation of the following data: 20, 18, 32, 24,…
- If the coefficient of variation of a collection of data is 57 and its S.D is…
- A group of 100 candidates have their average height 163.8 cm with coefficient…
- Given sum x = 99 , n = 9 and sum (x-10)^2 = 79 . Find sum x^2sum (x - bar x)^2…
- The marks scored by two students A, B in a class are given below.…

**Exercise 11.2**- The range of the first 10 prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 isA.…
- The least value in a collection of data is 14.1. If the range of the collection…
- The greatest value of a collection of data is 72 and the least value is 28.…
- For a collection of 11 items, sum x = 132 , then the arithmetic mean isA. 11 B.…
- For any collection of n items, sum (x - bar x) =A. sum x B. bar x C. i bar x D.…
- For any collection of n items, (sum x) - bar x =A. i bar x B. (11-2) bar x C.…
- If t is the standard deviation of x, y. z, then the standard deviation of x +…
- If the standard deviation of a set of data is 1.6, then the variance isA. 0.4…
- If the variance of a data is 12.25, then the S.D isA. 3.5 B. 3 C. 2.5 D. 3.25…
- Variance of the first 11 natural numbers isA. root 5 B. root 10 C. 5 root 2 D.…
- The variance of 10, 10, 10, 10, 10 isA. 10 B. root 10 C. 5 D. 0
- If the variance of 14, 18, 22, 26, 30 is 32, then the variance of 28,…
- Standard deviation of a collection of data is 2√2. If each value is multiplied…
- Given sum (x - bar x) = 48 , bar x = 20 and n = 12. The coefficient of…
- Mean and standard deviation of a data are 48 and 12 respectively. The…

**Exercise 11.1**

- 59, 46, 30, 23, 27, 40, 52, 35, 29 Find the range and coefficient of range of…
- 41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5 Find the range and coefficient…
- The smallest value of a collection of data is 12 and the range is 59. Find the…
- The largest of 50 measurements is 3.84 kg. If the range is 0.46 kg, find the…
- The standard deviation of 20 observations is √5. If each observation is…
- Calculate the standard deviation of the first 13 natural numbers.…
- 10, 20, 15, 8, 3, 4 Calculate the standard deviation of the following data.…
- 38, 40, 34 ,31, 28, 26, 34 Calculate the standard deviation of the following…
- |c|c|c|c|c|c| x&3&8&13&18&23 y&7&10&15&10&8 Calculate the standard deviation of…
- The number of books bought at a book fair by 200 students from a school are…
- Calculate the variance of the following data |c|c|c|c|c|c|c|c|c|
- The time (in seconds) taken by a group of people to walk across a pedestrian…
- A group of 45 house owners contributed money towards green environment of…
- Find the variance of the following distribution. |c|c|c|c|c|c|c|c|…
- Mean of 100 items is 48 and their standard deviation is 10. Find the sum of…
- The mean and standard deviation of 20 items are found to be 10 and 2…
- If n = 10 , bar x = 12 and sum x^2 = 1530 , then calculate the coefficient of…
- Calculate the coefficient of variation of the following data: 20, 18, 32, 24,…
- If the coefficient of variation of a collection of data is 57 and its S.D is…
- A group of 100 candidates have their average height 163.8 cm with coefficient…
- Given sum x = 99 , n = 9 and sum (x-10)^2 = 79 . Find sum x^2sum (x - bar x)^2…
- The marks scored by two students A, B in a class are given below.…

**Exercise 11.2**

- The range of the first 10 prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 isA.…
- The least value in a collection of data is 14.1. If the range of the collection…
- The greatest value of a collection of data is 72 and the least value is 28.…
- For a collection of 11 items, sum x = 132 , then the arithmetic mean isA. 11 B.…
- For any collection of n items, sum (x - bar x) =A. sum x B. bar x C. i bar x D.…
- For any collection of n items, (sum x) - bar x =A. i bar x B. (11-2) bar x C.…
- If t is the standard deviation of x, y. z, then the standard deviation of x +…
- If the standard deviation of a set of data is 1.6, then the variance isA. 0.4…
- If the variance of a data is 12.25, then the S.D isA. 3.5 B. 3 C. 2.5 D. 3.25…
- Variance of the first 11 natural numbers isA. root 5 B. root 10 C. 5 root 2 D.…
- The variance of 10, 10, 10, 10, 10 isA. 10 B. root 10 C. 5 D. 0
- If the variance of 14, 18, 22, 26, 30 is 32, then the variance of 28,…
- Standard deviation of a collection of data is 2√2. If each value is multiplied…
- Given sum (x - bar x) = 48 , bar x = 20 and n = 12. The coefficient of…
- Mean and standard deviation of a data are 48 and 12 respectively. The…

###### Exercise 11.1

**Question 1.**Find the range and coefficient of range of the following data.

59, 46, 30, 23, 27, 40, 52, 35, 29

**Answer:**Given the set of data 59, 46, 30, 23, 27, 40, 52, 35, 29.

Let the maximum value in the data set be denoted by x_{max} and minimum by x_{min}

Range = Maximum value in the data set – Minimum value in the data set

= x_{max} - x_{min}

= 59 – 23

= 36

∴ Range R = 36

Let the Coefficient of Range be denoted by s.

s =

=

=

= 0.439≈0.44

∴ s = 0.44

**Question 2.**Find the range and coefficient of range of the following data.

41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5

**Answer:**Given the set of data 41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5.

Let the maximum value in the data set be denoted by x_{max} and minimum by x_{min}

Range = Maximum value in the data set – Minimum value in the data set

= x_{max} - x_{min}

= 56.5 – 12.5

= 44

∴ Range R = 44

Let the Coefficient of Range be denoted by s.

s =

=

=

= 0.637≈0.64

∴ s = 0.64

**Question 3.**The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data.

**Answer:**Given x_{min} = 12, R = 59

Range R = x_{max} - x_{min}

Substituting the given terms into the above formula, we get

R = x_{max} - x_{min}

59 = x_{max} - 12

x_{max} = 59 + 12 = 71

**Question 4.**The largest of 50 measurements is 3.84 kg. If the range is 0.46 kg, find the smallest measurement.

**Answer:**Given x_{max} = 3.84kg, R = 0.46kg

Range R = x_{max} - x_{min}

Substituting the given terms into the above formula, we get

R = x_{max} - x_{min}

0.46 = 3.84- x_{min}

x_{min} = 3.84 - 0.46 = 3.38kg

**Question 5.**The standard deviation of 20 observations is √5. If each observation is multiplied by 2, find the standard deviation and variance of the resulting observations.

**Answer:**Let the observations be x_{1}, x_{2}, x_{3}….x_{20}

Given SD =

Formula for SD =

Where N = 20, SD =

If each observation is multiplied by 2, we get new set of observations.

Let the new observations be y_{1}, y_{2}, y_{3}….y_{20}

New Standard Deviation SD’ =

We know that and

But y_{i} = 2x_{i}

Therefore,

Substituting in the SD’ formula,

SD’ =

=

= 2 × SD = 2

Formula relating SD and Variance is Variance = SD^{2}

So Variance = (2^{2} = 20

**Question 6.**Calculate the standard deviation of the first 13 natural numbers.

**Answer:**To find

Formula for

=

SD =

= 3.74

**Question 7.**Calculate the standard deviation of the following data.

10, 20, 15, 8, 3, 4

**Answer:**To find

Formula for

=

SD =

= 5.97

**Question 8.**Calculate the standard deviation of the following data.

38, 40, 34 ,31, 28, 26, 34

**Answer:**To find

Formula for

=

SD =

= 4.69

**Question 9.**Calculate the standard deviation of the following data.

**Answer:**

To find

Formula for

=

SD =

=

= 6.32

**Question 10.**The number of books bought at a book fair by 200 students from a school are given in the following table.

Calculate the standard deviation.

**Answer:**

To find

Formula for

=

SD =

=

= 1.107

**Question 11.**Calculate the variance of the following data

**Answer:**

To find

Formula for

=

SD =

=

= 3.88

To find Variance

Variance = SD^{2}

= 3.88^{2} = 15.058

**Question 12.**The time (in seconds) taken by a group of people to walk across a pedestrian crossing is given in the table below.

Calculate the variance and standard deviation of the data.

**Answer:**

To find

Formula for

=

SD =

=

= 6.063

To find Variance

Variance = SD^{2}

= 6.063^{2} = 36.76

**Question 13.**A group of 45 house owners contributed money towards green environment of their street. The amount of money collected is shown in the table below.

Calculate the variance and standard deviation.

**Answer:**

To find

Formula for

=

SD =

=

= 20.39

To find Variance

Variance = SD^{2}

= 20.39^{2} = 416

**Question 14.**Find the variance of the following distribution.

**Answer:**

To find

Formula for

=

SD =

=

= 7.361

To find Variance

Variance = SD^{2}

= 7.361^{2} = 54.19

**Question 15.**Mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and the sum of the squares of all the items.

**Answer:**Mean of 100 items = 48

Standard deviation SD = 10

To find :

__To find__ :

Formula for

= 48 =

Sum of all the items

__To find____:__

SD^{2} =

100 = 48^{2}

240400

**Question 16.**The mean and standard deviation of 20 items are found to be 10 and 2 respectively. At the time of checking it was found that an item 12 was wrongly entered as 8. Calculate the correct mean and standard deviation.

**Answer:**Mean of 20 items = 10

SD of 10 items = 2

Wrong Value = 8

Correct Value = 12

__To find Mean:__

Formula for

= 10 =

Sum of all the items 200

This value is wrong since item 12 was wrongly entered as 8.

Let be the corrected sum

200 + (Correct Value) - (Wrong Value)

= 200 + 12 - 8 = 204

Corrected mean will be = 10.2

__To find SD:__

SD^{2} =

4 =

= 2080

This value is wrong since item 12 was wrongly entered as 8.

Let be the corrected sum of squares.

= 2080 + (Correct Value)^{2} - (Wrong Value)^{2}

= 2080 + 12^{2} - 8^{2}

= 2160

__Corrected SD:__

SD^{2} =

SD^{2} =

SD = 1.99

The corrected mean is 10.2, corrected SD is 1.99

**Question 17.**

**Answer:**SD^{2} =

SD^{2} =

SD = 3

Coefficient of Variation

CV =

= = 25

**Question 18.**Calculate the coefficient of variation of the following data: 20, 18, 32, 24, 26.

**Answer:**To find

Formula for

= 24

SD =

= 4.89

CV =

= 20.41

**Question 19.**If the coefficient of variation of a collection of data is 57 and its S.D is 6.84, then find the mean.

**Answer:**Given SD = 6.84 and CV = 57, to find

CV =

= 57

12

**Question 20.**A group of 100 candidates have their average height 163.8 cm with coefficient of variation 3.2. What is the standard deviation of their heights?

**Answer:**Given N = 100, CV = 3.2, = 163.8 cm

CV =

= 3.2

5.24

**Question 21.**Given and . Find .

**Answer:**SD =

Or SD^{2} =

To find

=

SD^{2} = =

Expanding the numerator in the form of (a - b)^{2} = a^{2} + b^{2} - 2ab,

SD^{2} = =

Substituting all the known terms in the above equation,

SD^{2} = = 7.77

We know that, SD^{2} =

7.77 =

= 1159

SD^{2} = = 7.77

= 70

**Question 22.**The marks scored by two students A, B in a class are given below.

Who is more consistent?

**Answer:**__SD of A__

= 60

SD =

SD_{A} = 5.4

__SD of B__

= 64

SD =

SD_{B} = 6.7

5.4<6.7

SD of A is less than SD of B.

A is more consistent than B

**Question 1.**

Find the range and coefficient of range of the following data.

59, 46, 30, 23, 27, 40, 52, 35, 29

**Answer:**

Given the set of data 59, 46, 30, 23, 27, 40, 52, 35, 29.

Let the maximum value in the data set be denoted by x_{max} and minimum by x_{min}

Range = Maximum value in the data set – Minimum value in the data set

= x_{max} - x_{min}

= 59 – 23

= 36

∴ Range R = 36

Let the Coefficient of Range be denoted by s.

s =

=

=

= 0.439≈0.44

∴ s = 0.44

**Question 2.**

Find the range and coefficient of range of the following data.

41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5

**Answer:**

Given the set of data 41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5.

Let the maximum value in the data set be denoted by x_{max} and minimum by x_{min}

Range = Maximum value in the data set – Minimum value in the data set

= x_{max} - x_{min}

= 56.5 – 12.5

= 44

∴ Range R = 44

Let the Coefficient of Range be denoted by s.

s =

=

=

= 0.637≈0.64

∴ s = 0.64

**Question 3.**

The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data.

**Answer:**

Given x_{min} = 12, R = 59

Range R = x_{max} - x_{min}

Substituting the given terms into the above formula, we get

R = x_{max} - x_{min}

59 = x_{max} - 12

x_{max} = 59 + 12 = 71

**Question 4.**

The largest of 50 measurements is 3.84 kg. If the range is 0.46 kg, find the smallest measurement.

**Answer:**

Given x_{max} = 3.84kg, R = 0.46kg

Range R = x_{max} - x_{min}

Substituting the given terms into the above formula, we get

R = x_{max} - x_{min}

0.46 = 3.84- x_{min}

x_{min} = 3.84 - 0.46 = 3.38kg

**Question 5.**

The standard deviation of 20 observations is √5. If each observation is multiplied by 2, find the standard deviation and variance of the resulting observations.

**Answer:**

Let the observations be x_{1}, x_{2}, x_{3}….x_{20}

Given SD =

Formula for SD =

Where N = 20, SD =

If each observation is multiplied by 2, we get new set of observations.

Let the new observations be y_{1}, y_{2}, y_{3}….y_{20}

New Standard Deviation SD’ =

We know that and

But y_{i} = 2x_{i}

Therefore,

Substituting in the SD’ formula,

SD’ =

=

= 2 × SD = 2

Formula relating SD and Variance is Variance = SD^{2}

So Variance = (2^{2} = 20

**Question 6.**

Calculate the standard deviation of the first 13 natural numbers.

**Answer:**

To find

Formula for

=

SD =

= 3.74

**Question 7.**

Calculate the standard deviation of the following data.

10, 20, 15, 8, 3, 4

**Answer:**

To find

Formula for

=

SD =

= 5.97

**Question 8.**

Calculate the standard deviation of the following data.

38, 40, 34 ,31, 28, 26, 34

**Answer:**

To find

Formula for

=

SD =

= 4.69

**Question 9.**

Calculate the standard deviation of the following data.

**Answer:**

To find

Formula for

=

SD =

=

= 6.32

**Question 10.**

The number of books bought at a book fair by 200 students from a school are given in the following table.

Calculate the standard deviation.

**Answer:**

To find

Formula for

=

SD =

=

= 1.107

**Question 11.**

Calculate the variance of the following data

**Answer:**

To find

Formula for

=

SD =

=

= 3.88

To find Variance

Variance = SD^{2}

= 3.88^{2} = 15.058

**Question 12.**

The time (in seconds) taken by a group of people to walk across a pedestrian crossing is given in the table below.

Calculate the variance and standard deviation of the data.

**Answer:**

To find

Formula for

=

SD =

=

= 6.063

To find Variance

Variance = SD^{2}

= 6.063^{2} = 36.76

**Question 13.**

A group of 45 house owners contributed money towards green environment of their street. The amount of money collected is shown in the table below.

Calculate the variance and standard deviation.

**Answer:**

To find

Formula for

=

SD =

=

= 20.39

To find Variance

Variance = SD^{2}

= 20.39^{2} = 416

**Question 14.**

Find the variance of the following distribution.

**Answer:**

To find

Formula for

=

SD =

=

= 7.361

To find Variance

Variance = SD^{2}

= 7.361^{2} = 54.19

**Question 15.**

Mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and the sum of the squares of all the items.

**Answer:**

Mean of 100 items = 48

Standard deviation SD = 10

To find :

__To find__ :

Formula for

= 48 =

Sum of all the items

__To find____:__

SD^{2} =

100 = 48^{2}

240400

**Question 16.**

The mean and standard deviation of 20 items are found to be 10 and 2 respectively. At the time of checking it was found that an item 12 was wrongly entered as 8. Calculate the correct mean and standard deviation.

**Answer:**

Mean of 20 items = 10

SD of 10 items = 2

Wrong Value = 8

Correct Value = 12

__To find Mean:__

Formula for

= 10 =

Sum of all the items 200

This value is wrong since item 12 was wrongly entered as 8.

Let be the corrected sum

200 + (Correct Value) - (Wrong Value)

= 200 + 12 - 8 = 204

Corrected mean will be = 10.2

__To find SD:__

SD^{2} =

4 =

= 2080

This value is wrong since item 12 was wrongly entered as 8.

Let be the corrected sum of squares.

= 2080 + (Correct Value)^{2} - (Wrong Value)^{2}

= 2080 + 12^{2} - 8^{2}

= 2160

__Corrected SD:__

SD^{2} =

SD^{2} =

SD = 1.99

The corrected mean is 10.2, corrected SD is 1.99

**Question 17.**

**Answer:**

SD^{2} =

SD^{2} =

SD = 3

Coefficient of Variation

CV =

= = 25

**Question 18.**

Calculate the coefficient of variation of the following data: 20, 18, 32, 24, 26.

**Answer:**

To find

Formula for

= 24

SD =

= 4.89

CV =

= 20.41

**Question 19.**

If the coefficient of variation of a collection of data is 57 and its S.D is 6.84, then find the mean.

**Answer:**

Given SD = 6.84 and CV = 57, to find

CV =

= 57

12

**Question 20.**

A group of 100 candidates have their average height 163.8 cm with coefficient of variation 3.2. What is the standard deviation of their heights?

**Answer:**

Given N = 100, CV = 3.2, = 163.8 cm

CV =

= 3.2

5.24

**Question 21.**

Given and . Find .

**Answer:**

SD =

Or SD^{2} =

To find

=

SD^{2} = =

Expanding the numerator in the form of (a - b)^{2} = a^{2} + b^{2} - 2ab,

SD^{2} = =

Substituting all the known terms in the above equation,

SD^{2} = = 7.77

We know that, SD^{2} =

7.77 =

= 1159

SD^{2} = = 7.77

= 70

**Question 22.**

The marks scored by two students A, B in a class are given below.

Who is more consistent?

**Answer:**

__SD of A__

= 60

SD =

SD_{A} = 5.4

__SD of B__

= 64

SD =

SD_{B} = 6.7

5.4<6.7

SD of A is less than SD of B.

A is more consistent than B

###### Exercise 11.2

**Question 1.**The range of the first 10 prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 is

A. 28

B. 26

C. 29

D. 27

**Answer:**Range R = x_{max} - x_{min}

R = 29 - 2 = 27

So the correct option is D.

**Question 2.**The least value in a collection of data is 14.1. If the range of the collection is 28.4, then the greatest value of the collection is

A. 42.5

B. 43.5

C. 42.4

D. 42.1

**Answer:**Given x_{min} = 14.1, R = 28.4

Range R = x_{max} - x_{min}

28.4 = x_{max} - 14.1

x_{max} = 42.5

So the correct option is A.

**Question 3.**The greatest value of a collection of data is 72 and the least value is 28. Then the coefficient of range is

A. 44

B. 0.72

C. 0.44

D. 0.28

**Answer:**Given x_{max} = 72, x_{min} = 28

Coefficient of range s =

=

So the correct option is C.

**Question 4.**For a collection of 11 items, , then the arithmetic mean is

A. 11

B. 12

C. 14

D. 13

**Answer:**N = 11

AM

So the correct option is B.

**Question 5.**For any collection of n items, =

A.

B.

C.

D. 0

**Answer:** can be rewritten as

We know that so

Also, because is just a constant term.

Substituting these in , we get = 0

So the correct option is D.

**Question 6.**For any collection of n items, =

A.

B.

C.

D. 0

**Answer:**We know that so

Substituting this in the question, we have

So the correct option is C.

**Question 7.**If t is the standard deviation of x, y. z, then the standard deviation of x + 5, y + 5, z + 5 is

A.

B. t + 5

C. t

D. x y z

**Answer:**It is a direct consequence of the theory of standard deviation that, the same constant term added to the terms in a set of data doesn’t change the value of standard deviation.

So the correct answer is t and correct option is C.

**Question 8.**If the standard deviation of a set of data is 1.6, then the variance is

A. 0.4

B. 2.56

C. 1.96

D. 0.04

**Answer:**Variance = SD^{2}

So Variance = 1.6^{2} = 2.56

Therefore, the correct option is B.

**Question 9.**If the variance of a data is 12.25, then the S.D is

A. 3.5

B. 3

C. 2.5

D. 3.25

**Answer:**Variance = SD^{2}

Or SD =

SD = 3.5

So the correct option is A.

**Question 10.**Variance of the first 11 natural numbers is

A.

B.

C.

D. 10

**Answer:**Variance of first n natural numbers is given by

V = 10

So the correct option is D.

**Question 11.**The variance of 10, 10, 10, 10, 10 is

A. 10

B.

C. 5

D. 0

**Answer:**Standard deviation of a constant set of data is 0.

We know that Variance = SD^{2}

Variance = 0

So the correct option is D.

**Question 12.**If the variance of 14, 18, 22, 26, 30 is 32, then the variance of 28, 36,44,52,60 is

A. 64

B. 128

C. 32√2

D. 32

**Answer:**Two data sets are given.

Set A : 14, 18, 22, 26, 30 with V = 32

Set B : 28, 36, 44, 52, 60 with V = ?

We notice that each data entry in set B is twice the corresponding data entry in set A.

SD of set B = 2 × SD of set A.

We know that Variance = SD^{2}

Variance of Set B = 2^{2} × Variance of Set A.

= 4 × 32 = 128.

So the correct option is B.

**Question 13.**Standard deviation of a collection of data is 2√2. If each value is multiplied by 3, then the standard deviation of the new data is

A.

B. 4√2

C. 6√2

D. 9√2

**Answer:**SD of set B = n × SD of set A, where n is the data multiplier

Here, n = 3.

So, SD of set B = 3 × SD of set A = 3 × 2 = 6

So, the correct option is C.

**Question 14.**Given and n = 12. The coefficient of variation is

A. 25

B. 20

C. 30

D. 10

**Answer:**Insufficient data.

**Question 15.**Mean and standard deviation of a data are 48 and 12 respectively. The coefficient of variation is

A. 42

B. 25

C. 28

D. 48

**Answer:**CV =

CV =

So, the correct option is B.

**Question 1.**

The range of the first 10 prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 is

A. 28

B. 26

C. 29

D. 27

**Answer:**

Range R = x_{max} - x_{min}

R = 29 - 2 = 27

So the correct option is D.

**Question 2.**

The least value in a collection of data is 14.1. If the range of the collection is 28.4, then the greatest value of the collection is

A. 42.5

B. 43.5

C. 42.4

D. 42.1

**Answer:**

Given x_{min} = 14.1, R = 28.4

Range R = x_{max} - x_{min}

28.4 = x_{max} - 14.1

x_{max} = 42.5

So the correct option is A.

**Question 3.**

The greatest value of a collection of data is 72 and the least value is 28. Then the coefficient of range is

A. 44

B. 0.72

C. 0.44

D. 0.28

**Answer:**

Given x_{max} = 72, x_{min} = 28

Coefficient of range s =

=

So the correct option is C.

**Question 4.**

For a collection of 11 items, , then the arithmetic mean is

A. 11

B. 12

C. 14

D. 13

**Answer:**

N = 11

AM

So the correct option is B.

**Question 5.**

For any collection of n items, =

A.

B.

C.

D. 0

**Answer:**

can be rewritten as

We know that so

Also, because is just a constant term.

Substituting these in , we get = 0

So the correct option is D.

**Question 6.**

For any collection of n items, =

A.

B.

C.

D. 0

**Answer:**

We know that so

Substituting this in the question, we have

So the correct option is C.

**Question 7.**

If t is the standard deviation of x, y. z, then the standard deviation of x + 5, y + 5, z + 5 is

A.

B. t + 5

C. t

D. x y z

**Answer:**

It is a direct consequence of the theory of standard deviation that, the same constant term added to the terms in a set of data doesn’t change the value of standard deviation.

So the correct answer is t and correct option is C.

**Question 8.**

If the standard deviation of a set of data is 1.6, then the variance is

A. 0.4

B. 2.56

C. 1.96

D. 0.04

**Answer:**

Variance = SD^{2}

So Variance = 1.6^{2} = 2.56

Therefore, the correct option is B.

**Question 9.**

If the variance of a data is 12.25, then the S.D is

A. 3.5

B. 3

C. 2.5

D. 3.25

**Answer:**

Variance = SD^{2}

Or SD =

SD = 3.5

So the correct option is A.

**Question 10.**

Variance of the first 11 natural numbers is

A.

B.

C.

D. 10

**Answer:**

Variance of first n natural numbers is given by

V = 10

So the correct option is D.

**Question 11.**

The variance of 10, 10, 10, 10, 10 is

A. 10

B.

C. 5

D. 0

**Answer:**

Standard deviation of a constant set of data is 0.

We know that Variance = SD^{2}

Variance = 0

So the correct option is D.

**Question 12.**

If the variance of 14, 18, 22, 26, 30 is 32, then the variance of 28, 36,44,52,60 is

A. 64

B. 128

C. 32√2

D. 32

**Answer:**

Two data sets are given.

Set A : 14, 18, 22, 26, 30 with V = 32

Set B : 28, 36, 44, 52, 60 with V = ?

We notice that each data entry in set B is twice the corresponding data entry in set A.

SD of set B = 2 × SD of set A.

We know that Variance = SD^{2}

Variance of Set B = 2^{2} × Variance of Set A.

= 4 × 32 = 128.

So the correct option is B.

**Question 13.**

Standard deviation of a collection of data is 2√2. If each value is multiplied by 3, then the standard deviation of the new data is

A.

B. 4√2

C. 6√2

D. 9√2

**Answer:**

SD of set B = n × SD of set A, where n is the data multiplier

Here, n = 3.

So, SD of set B = 3 × SD of set A = 3 × 2 = 6

So, the correct option is C.

**Question 14.**

Given and n = 12. The coefficient of variation is

A. 25

B. 20

C. 30

D. 10

**Answer:**

Insufficient data.

**Question 15.**

Mean and standard deviation of a data are 48 and 12 respectively. The coefficient of variation is

A. 42

B. 25

C. 28

D. 48

**Answer:**

CV =

CV =

So, the correct option is B.