# Chapter 15 Statistics Ex – 15.2

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

Question 1.

6, 7, 10, 12, 13, 4, 8, 12

Solution:

Here xi = 6, 7, 10, 12, 13, 4, 8, 12
∴ Σxi = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72
n = 8

Question 2.

First n natural numbers

Solution:

Here xi = 1, 2, 3, 4, ……….n

Question 3.

First 10 multiples of 3

Solution:

Here xi = 3, 6, 9, 12, 15, 18, 21, 27, 30,
Σxi = 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 165
n = 10

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Find the mean and standard deviation using short-cut method

Solution:

Find the mean and variance for the following frequency distributions in Exercises 7 and 8.

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Find the mean, variance and standard deviation using short-cut method.

Solution:

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.

[Hint: First make the data continuous by making the classes as 32.5 – 36.5, 36.5 – 40.5, 40.5 – 44.5, 44.5 – 48.5, 48.5 – 52.5 and then proceed.]

Solution: