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Mean

Calculate the...

Question

Calculate the standard deviation for the following data:
Class - internal Frequency
$1 - 5$
$6 - 10$
$11 - 15$
$16 - 20$ $4$
$3$
$2$
$1$
$N = 10$

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Solution

$C . I .$ $f$ $x$ $f x$ $x - ¯ ¯ ¯ x = D$ $D^{2}$ $f D^{2}$
$1 - 5$ $4$ $3$ $12$ $- 5$ $25$ $100$
$6 - 10$ $3$ $8$ $24$ $0$ $00$ $00$
$11 - 15$ $2$ $13$ $26$ $5$ $25$ $50$
$16 - 20$ $1$ $18$ $18$ $10$ $100$ $100$

$N = 10, \sum f x = 80, \sum f D^{2} = 250$

Mean $¯ ¯ ¯ x = \frac{\sum f x}{N} = \frac{80}{10} = 8$

$σ = \sqrt{\frac{\sum f D^{2}}{N}} = \sqrt{\frac{250}{10}} = \sqrt{25} = 5$

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