Question

For the following distribution, calculate mean using all suitable methods:

Size of items:	1 - 4	4 - 9	9 - 16	16 - 27
Frequency:	6	12	26	20

Answer 1

By direct method

Class interval	Mid value (xi)	Frequency (fi)	fixi
1 - 4	2.5	6	15
4 - 9	6.5	12	78
9 - 16	12.5	26	325
16 - 27	21.5	20	430
		N = 64	\(\sum\)fiui = 848

Mean \(=\frac{\sum f_ix_i}{N}+A\) 

\(=\frac{848}{64} = 13.25\)

By assumed mean method

Let, 

the assumed mean (A) = 6.5

Class interval	Mid value (xi)	ui = xi - A = xi - 6.5	Frequency (fi)	fiui
1 - 4	2.5	-4	6	-24
4 - 9	6.5	0	12	0
9 - 16	12.5	6	26	156
16 - 27	21.5	15	20	300
			N = 64	\(\sum\)fiui = 432

Mean = A + \(\frac{\sum f_iu_i}{N}\)

\(=6.5+\frac{432}{64}\)

\(=6.5+6.75\)

\(=13.25\)