The marks scored by 5 students in a class are 25, 30, 35, 40 and 45. Find the standard deviation using Assumed mean method.

7.07

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3.21

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8.12

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6.12

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Solution

The correct option is A 7.07
The mean of the marks = 35
Hence, we take assumed mean, A = 35.
$\begin{matrix} x i & d i = x i - A & d i^{2} = x i - 35 25 & - 10 & 100 30 & - 5 & 25 35 & 0 & 0 40 & 5 & 25 45 & 10 & 100 \sum d i = 0 & \sum d i^{2} = 250 \end{matrix}$ .

Standard Deviation

$σ = \sqrt{\frac{\sum d i^{2}}{n} - (\frac{\sum d i}{n})^{2}}$

$= \sqrt{\frac{250}{5} - \frac{0}{5}} = \sqrt{50} ≃ 7.07$

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Similar questions

\begin{matrix} x & 4 & 6 & 8 & 10 & 12 f & 7 & 3 & 5 & 9 & 5 \end{matrix}

Marks:	0−10	10−20	20−30	30−40	40−50
Number of students:	20	24	40	36	20

140

Marks:	0-10	10-20	20-30	30-40	40-50
Number of students:	$20$	$24$	$40$	$36$	$20$

60

Marks	$5 - 15$	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$
No. of students	$8$	$12$	$20$	$10$	$7$	$3$

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