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.

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:

∴ 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

Question 2.
First n natural numbers.
Answer:
Sum of first n natural number = 1 + 2 + 3 + 4 + .................. n.

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

Thus, mean of first 10 multiples of 3 = 16.5
and
Variance = 74.25

Question 4.
Find mean and variance:
Answer:

= 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:
Answer:

Thus, mean of given frequency distribution = 100
and Variance = 29.09

Question 6.
Find mean and standard deviation using short-cut method:
Answer:
Let assumed mean A = 63
Thus, 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.
Answer:

Thus, mean of given frequency distribution = 107
and Variance (σ²) = 2276

Question 8.
Answer:
Question 9.
Find mean, variance and standard deviation by short-cut method:
Answer:


Thus, standard deviation σ = √105.58 = 10.27
Thus, mean of given frequency distribution = 93
Variance = 105.58
and standard deviation = 10.27

Question 10.
The diameters of circles (in mm) drawn in a design are given below:
Calculate 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.