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

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

To do:

We have to calculate mean using all suitable methods.

Solution:

Let the assumed mean be $A=12.5$.

Using direct method, we get,

 We know that,

Mean $=\frac{\sum{f_ix_i}}{\sum{f_i}}$    

Therefore,  

Mean $=\frac{848}{64}$

$=13.25$

Using shortcut method, we get,

Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$    

Therefore,  

Mean $=12.5+\frac{48}{64}$

$=12.5+\frac{3}{4}$

$=12.5+0.75$

$=13.25$

The mean of the given distribution is $13.25$.

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Updated on: 10-Oct-2022

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