Find the mean and standard deviation using short-cut method

xi 60 61 62 63 64 65 66 67 68
fi 2 1 12 29 25 12 10 4 5

 

 

Asked by Abhisek | 11 months ago |  74

1 Answer

Solution :-

\( \overline{x}= A +\dfrac{\displaystyle\sum_{i=1}{f_i}u_i }{N}× h\)

Where A = 64, h = 1

So, x̅ = 64 + ((\( \dfrac{0}{100}\)) × 1)

= 64 + 0

= 64

Then, variance,

\( σ^2= \dfrac{h^2}{N^2}[N\displaystyle\sum_{i=1}{f_i}u_i^2-(\displaystyle\sum_{i=1}{f_i}u_i)^2] \)

σ2 = (\( \dfrac{1^2}{100^2}\)) [100(286) – 02]

= (\( \dfrac{1}{10000}\)) [28600 – 0]

\( \dfrac{28600}{10000}\)

= 2.86

Hence, standard deviation = σ =\( \sqrt{2.886}\)

= 1.691

Mean = 64 and Standard Deviation = 1.691

Answered by Abhisek | 11 months ago

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