Using the same marks distribution as Worked Example 8, find the standard deviation by the step-deviation metho

Worked Examples · Example 9

Using the same marks distribution as Worked Example 8, find the standard deviation by the step-deviation method (taking $A=25$ , $h=10$ ), and verify it agrees with Worked Example 8's answer.

Marks	0–10	10–20	20–30	30–40	40–50
Number of students ( $f$ )	4	6	14	10	6

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Step 1 — Compute $u=(x-25)/10$ and $fu$ , $fu^2$ for each class.

Class	$f$	$x$	$u=(x-25)/10$	$fu$	$fu^2$
0–10	4	5	−2	−8	16
10–20	6	15	−1	−6	6
20–30	14	25	0	0	0
30–40	10	35	1	10	10
40–50	6	45	2	12	24
Total	40			8	56

Step 2 — Apply the step-deviation formula.

$\sigma = h\times\sqrt{\dfrac{\sum fu^2}{N} - \left(\dfrac{\sum fu}{N}\right)^2} = 10\times\sqrt{\dfrac{56}{40} - \left(\dfrac{8}{40}\right)^2} = 10\times\sqrt{1.4-0.04} = 10\times\sqrt{1.36} \approx 10\times1.1662 \approx 11.66$ …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set ANNUAL1 markMCQ
$Q. If the variance of the data is 144 then the standard deviation of the data is$
(a) 144
(b) -12
(c) 12
(d) 14
›Reveal solutionSolution

Standard deviation is defined as the positive square root of variance.

By definition, standard deviation $\sigma = \sqrt{\text{variance}}$ . Given variance $= 144$ :

$\sigma = \sqrt{144} = 12$ …

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CBSE 2026Set ANNUAL1 markMCQ
$Q. The square of standard deviation is —$
(a) Mean-deviation
(b) Range
(c) Variance
(d) Mean
›Reveal solutionSolution

The square of the standard deviation is called the variance, option (c).

Standard deviation ( $\sigma$ ) measures the spread of data about the mean. By definition, variance ( $\sigma^2$ ) is exactly the square of the standard deviation: $\text{Variance} = \sigma^2 = (\text{Standard Deviation})^2$ .

…

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CBSE 2026Set ANNUAL1 mark
$Q. Fill in the blank: If variance of given data is 225, then the standard deviation of the same data will be ______.$
›Reveal solutionSolution

Standard deviation $=\sqrt{\text{Variance}}$ ; here $\sqrt{225}=15$ .

By definition, variance is the square of the standard deviation, so standard deviation $=\sqrt{\text{variance}}$ .

…

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CBSE 2024Set ANNUAL1 markMCQ
$Q. If the standard deviation of a data is 0.012, find the variance.$
(a) 0.144
(b) 0.00144
(c) 0.000144
(d) None of these
›Reveal solutionSolution

Variance is defined as the square of the standard deviation.

By definition, variance $= (\text{standard deviation})^2$ .

Given standard deviation $= 0.012$ : …

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CBSE 2024Set ANNUAL1 mark
$Q. If the standard deviation of obtained marks of a class students is 1.6, then find the variance.$
›Reveal solutionSolution

Given standard deviation $=1.6$ , the variance is $2.56$ .

By definition, variance $=(\text{standard deviation})^2$ . Here standard deviation $=1.6$ …

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CBSE 2024Set ANNUAL1 mark
$Q. Fill in the blank: In a series, the difference between the maximum value and the minimum value is called ______.$
›Reveal solutionSolution

This difference is called the range of the series, the simplest measure of dispersion.

Step 1. Range is defined as: Range $=$ Maximum value $-$ Minimum value.

…

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