Calculate the standard deviation of the following data.
$x$ $3$ $8$ $13$ $18$ $23$
$f$ $7$ $10$ $15$ $10$ $8$

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Solution

$¯ x = \frac{\sum F x}{\sum F} = \frac{660}{50} = 132$
$σ = \sqrt{\frac{\sum F {(x_{i} - ¯ x)}^{2}}{\sum F - 1}} = \sqrt{\frac{1998}{49}} = 6.38$

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Similar questions

X	$10$	$11$	$12$	$13$	$14$	$15$	$16$	$17$	$18$
f	$2$	$7$	$10$	$12$	$15$	$11$	$10$	$6$	$3$

\begin{matrix} x_{i} & 3 & 8 & 13 & 18 & 23 f_{i} & 7 & 10 & 15 & 10 & 6 \end{matrix}

X	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
f	$10$	$8$	$15$	$8$	$4$

48

Data x	$6$	$7$	$8$	$9$	$10$	$11$	$12$
Frequency f	$5$	$6$	$9$	$13$	$8$	$5$	$4$

10, 20, 15, 8, 3, 4

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