1.

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»

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 20430
 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 2.5-46-24
 4 - 9 6.50120
 9 - 16 12.5 626156
 16 - 27 21.5 15 20 300
 N = 64\(\sum\)fiui = 432


Mean = A + \(\frac{\sum f_iu_i}{N}\)

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

\(=6.5+6.75\)

\(=13.25\) 


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