RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2

Rajasthan Board RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Textbook Exercise Questions and Answers.

Rajasthan Board RBSE Solutions for Class 11 Maths in Hindi Medium & English Medium are part of RBSE Solutions for Class 11. Students can also read RBSE Class 11 Maths Important Questions for exam preparation. Students can also go through RBSE Class 11 Maths Notes to understand and remember the concepts easily.

RBSE Class 11 Maths Solutions Chapter 15 Statistics Ex 15.2

Find mean and variance for each of the data in Exercises 1 to 5.

Question 1.
6, 7, 10, 12, 13, 4, 8, 12
Answer:
Mean of given data:

Term xi

Deviation from Mean (x̄ = 9)
di = (xi - x̄)

di2 = (xi – x̄)2

6

6 – 9 = - 3

+ 9

7

7 – 9 = - 2

+ 4

10

10 – 9 = +1

+ 1

12

12 – 9 = + 3

+ 9

13

13 – 9 = + 4

+ 16

4

4 – 9 = - 5

+ 25

8

8 – 9 = - 1

+ 1

12

12 – 9 = + 3

+ 9

Total = 72, n = 8

 

\(\sum_{i=1}^8\) (xi – x̄)2 = 74

∴ variance σ2 = \(\frac{\sum_{i=1}^8\left(x_i-\bar{x}\right)^2}{N}\) = \(\frac{74}{8}\) = 9.25
Thus, mean of given data = 9 and variance = 9.25

RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2

Question 2.
First n natural numbers.
Answer:
Sum of first n natural number = 1 + 2 + 3 + 4 + .................. n.
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 1
Thus, mean of first n natural numbers x̄ = \(\frac{n+1}{2}\)
and variance of first n natural numbers σ2 = \(\frac{n^2-1}{12}\)

Question 3.
First 10 multiples of 30.
Answer:
First 10 multiples of 3 are 3, 6, 9, 12, 15, 18, ........................., 30
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 2
Thus, mean of first 10 multiples of 3 = 16.5
and
Variance = 74.25

RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2

Question 4.
Find mean and variance:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 3Answer:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 4RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 5
= 404.4 - (19)2 = 404.4 - 361 = 43.4
Thus, mean of given frequency distribution = 19
and Variance = 43.4

Question 5.
Find mean and variance for the following frequency distribution:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 6Answer:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 7
Thus, mean of given frequency distribution = 100
and Variance = 29.09

RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2

Question 6.
Find mean and standard deviation using short-cut method:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 8Answer:
Let assumed mean A = 63
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 9Thus, mean of given frequency distribution = 64
and standard deviation = 1.69

Find mean and variance for the following frequency distribution In Exercises 7 and 8.

Question 7.
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 10Answer:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 11
Thus, mean of given frequency distribution = 107
and Variance (σ2) = 2276

RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2

Question 8.
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 12Answer:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 13Question 9.
Find mean, variance and standard deviation by short-cut method:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 14Answer:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 15
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 16
Thus, standard deviation σ = √105.58 = 10.27
Thus, mean of given frequency distribution = 93
Variance = 105.58
and standard deviation = 10.27

RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2

Question 10.
The diameters of circles (in mm) drawn in a design are given below:
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 17Calculate the standard deviation and mean diameter of the circles.
Answer:
Here class interval is not continuous.
Thus, first make the data continuous by subtracting 0.5 in the lower limit of each class and adding 0.5 in upper limit of each class.
RBSE Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 18

Bhagya
Last Updated on Nov. 18, 2023, 5:07 p.m.
Published Nov. 18, 2023