Find the variance of the following distribution.
Class interval $3.5 - 4.5$ $4.5 - 5.5$ $5.5 - 6.5$ $6.5 - 7.5$ $7.5 - 8.5$
Frequency $9$ $14$ $22$ $11$ $17$

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Solution

Let the assumed mean A be $6$ .
Class interval x mid values f $d = x - 6$ fd $f d^{2}$
$3.5 - 4.5$ $4$ $9$ $- 2$ $- 18$ $36$
$4.5 - 5.5$ $5$ $14$ $- 1$ $- 14$ $14$
$5.5 - 6.5$
$6$
$22$ $0$ $0$ $0$
$6.5 - 7.5$ $7$ $11$ $1$ $11$ $11$
$7.5 - 8.5$ $8$ $17$ $2$ $34$ $68$
$\sum f = 73$ $\sum f d = 13$ $\sum f d^{2} = 129$
Now variance, $σ^{2} = \frac{\sum f d^{2}}{\sum f} - {(\frac{\sum f d}{\sum f})}^{2}$
$= \frac{129}{73} = {(\frac{13}{73})}^{2} = \frac{129}{73} - \frac{169}{5329}$
$= \frac{9417 - 169}{5329} = \frac{9248}{5329}$
Thus, the variance is $σ^{2} ≃ 1.74$ .

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Class interval	$3.5 - 4.5$	$4.5 - 5.5$	$5.5 - 6.5$	$6.5 - 7.5$	$7.5 - 8.5$
Frequency	$9$	$14$	$22$	$11$	$17$

Find the variance of the following distribution.Class interval3.5−4.54.5−5.55.5−6.56.5−7.57.5−8.5Frequency914221117

Find the variance of the following distribution.
Class interval $3.5 - 4.5$ $4.5 - 5.5$ $5.5 - 6.5$ $6.5 - 7.5$ $7.5 - 8.5$
Frequency $9$ $14$ $22$ $11$ $17$