# For the following distribution, calculate mean using all suitable methods:  Size of items: 1 - 4, 4 - 9, 9 - 16, 16 - 27

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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

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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 + $\frac{\sum f_iu_i}{N}$

$=6.5+\frac{432}{64}$

$=6.5+6.75$

$=13.25$