Find the mean and variance for the following frequency distribution
Classes        0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequencies    2       3         5         10          3           5             2

Solution:

Let us draw the frequency table based on the given problem

Class	Frequency fi	Mid-point(xi)	yi = (xi - 105)/30	yi2	fiyi	fiyi2
0 - 30	2	15	- 3	9	- 6	18
30 - 60	3	45	- 2	4	- 6	12
60 - 90	5	75	- 1	1	- 5	5
90 - 120	10	105	0	0	0	0
120 - 150	3	135	1	1	3	3
150 - 180	5	165	2	4	10	20
180 - 210	2	195	3	9	6	18
					2	76

Mean,

x = A + [∑⁷_{i = 1} f_iy_i] / N × h

Here A = 105, N = 30 and h = 30

On substituting the value, we get

= 105 + 2/30 × 30

= 105 + 2

= 107

Variance,

(σ ²) = h² / N² [N ∑⁹_{i = 1}(f_iy_i)² - (∑⁹_{i = 1}f_iy_i)²]

On substituting the values, we get

= (30)² / (30)² [30 × 76 - (2)²]

= 2280 - 4

= 2276

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.2 Question 7

Find the mean and variance for the following frequency distribution Classes        0-30 30-60 60-90 90-120 120-150 150-180 180-210 Frequencies    2       3         5         10          3           5             2

Summary:

The mean and variance for the frequency distribution for the given data are 107 and 2276