Question

Find the mean, variance, and standard deviation from the sample data.

x f

0-3 42

4-7 84

8-11 55

12-15 83

16-19 112

20-23 24

Answer 1

Solution:

Class (1)	Frequency (f) (2)	Mid value (x) (3)	f⋅x (4)=(2)×(3)	f⋅x2=(f⋅x)×(x) (5)=(4)×(3)
0-3	42	1.5	63	94.5
4-7	84	5.5	462	2541
8-11	55	9.5	522.5	4963.75
12-15	83	13.5	1120.5	15126.75
16-19	112	17.5	1960	34300
20-23	24	21.5	516	11094
	n=400		∑f⋅x=4644	∑f⋅x2=68120

Mean ˉx=∑fxn

=4644/400

=11.61

Sample Variance S2=∑f⋅x2-(∑f⋅x)2nn-1

=68120-(4644)2400/399

=68120-53916.84/399

=14203.16/399

=35.5969

Sample Standard deviation S=√∑f⋅x2-(∑f⋅x)2nn-1

=√68120-(4644)2400/399

=√68120-53916.84/399

=√14203.16/399

=√35.5969

=5.9663