$x_{i}$ $10$ $15$ $18$ $20$ $25$
$f_{i}$ $3$ $2$ $5$ $8$ $2$
Find the Standard Deviation of the given data.

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4.34

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4.12

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4.05

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $4.12$
Mean, $u = \frac{\sum (f_{i} x_{i})}{\sum f_{i}} = \frac{360}{20} = 18$
$x_{i}$ $f_{i}$ $f_{i} x_{i}$ $x_{i} - u$ $(x_{i} - u)^{2}$ $f_{i} (x_{i} - u)^{2}$
$10$ $3$ $30$ $- 8$ $64$ $192$
$15$ $2$ $30$ $- 3$ $9$ $18$
$18$ $5$ $90$ $0$ $0$ $0$
$20$ $2$ $50$ $7$ $49$ $98$
$25$ $2$ $50$ $7$ $49$ $98$
$\sum f_{i} (x_{i} - u)^{2} = 340$ .
$∴ σ^{2} = \frac{1}{N} \times \sum f_{i} (x_{i} - u)^{2} = (\frac{1}{20} \times 340)$
$∴ σ^{2} = 17$
Now, Standard Deviation $S . D = \sqrt{σ^{2}}$
$∴ S . D = \sqrt{17}$
Thus $S . D = 4.12$

Suggest Corrections

Similar questions

$x_{i}$	$10$	$15$	$18$	$20$	$25$
$f_{i}$	$3$	$2$	$5$	$8$	$2$

x_{i}

f_{i}

$x_{i}$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_{i}$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

Find the mean deviation about the mean for the given data.

$\begin{matrix} x_{i} & 5 & 10 & 15 & 20 & 25 f_{i} & 7 & 4 & 6 & 3 & 5 \end{matrix}$

:

$X_{i}$	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$
$f_{i}$	$2$	$4$	$2$	$2$

Join BYJU'S Learning Program