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

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

By direct method

Class interval	Mid value (x_i)	Frequency (f_i)	f_ix_i
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	∑f_iu_i = 848

Mean =

= = 13.25

By assumed mean method

Let, the assumed mean (A) = 6.5

Class interval	Mid value (x_i)	u_i = x_i – A = x_i – 6.5	Frequency (f_i)	f_iu_i
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	∑f_iu_i = 432

Mean = A +

= 6.5 +

= 6.5 + 6.75

= 13.25

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