The following table gives weights of the students of two classes. Calculate the coefficient of variation of th

Exercise 8.3 · Q21

The following table gives weights of the students of two classes. Calculate the coefficient of variation of the two distributions. Which series is more variable?

Weight (in kg)	Class A	Class B
30-40	22	13
40-50	16	10
50-60	12	17

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Step 1 — Class A: mid-values 35, 45, 55 with frequencies 22, 16, 12 ( $N=50$ ). $\sum f_ix_i = 770+720+660=2150$ , so $\bar{x}_A=2150/50=43$ . $\sum f_ix_i^2 = 26950+32400+36300=95650$ , so $\text{Var}_A = 95650/50-43^2=64$ , giving $\sigma_A=8$ .

Step 2: $\text{C.V.}_A = 100\times8/43 \approx 18.60\%$ .

Step 3 — Class B: same mid-values with frequencies 13, 10, 17 ( $N=40$ ). $\sum f_ix_i = 455+450+935=1840$ , so $\bar{x}_B=1840/40=46$ . $\sum f_ix_i^2 = 15925+20250+51425=87600$ , so $\text{Var}_B = 87600/40-46^2=74$ , giving $\sigma_B=\sqrt{74}\approx8.60$ . …

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

CBSE 2024Set ANNUAL1 markMCQ
$Q. If mean and standard deviation of some numbers are 10 and 3 respectively, then their coefficient of variation, is :$
(a) 10%
(b) 20%
(c) 30%
(d) 40%
›Reveal solutionSolution

$CV=\dfrac{\sigma}{\bar{x}}\times100=\dfrac{3}{10}\times100=30\%$ .

The coefficient of variation expresses the standard deviation as a percentage of the mean: …

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CBSE 2023Set ANNUAL1 markMCQ
$Q. If the standard deviation and mean of a distribution are 5 and 20 respectively. The co-efficient of variation of the distribution is :$
(a) 4
(b) $\dfrac{1}{4}$
(c) 25%
(d) 20%
›Reveal solutionSolution

$\text{CV}=\dfrac{\sigma}{\bar{x}}\times 100=\dfrac{5}{20}\times 100=25\%$ .

Step 1 — the coefficient of variation is the relative measure

$\text{CV}=\dfrac{\sigma}{\bar{x}}\times 100$

…

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CBSE 2022Set ANNUAL1 markMCQ
$Q. If the mean and standard deviation are ₹75 and ₹15 respectively, then their coefficient of variation is :$
(a) $20\%$
(b) $33\frac{1}{3}\%$
(c) $40\%$
(d) $10\%$
›Reveal solutionSolution

$C.V.=\dfrac{\sigma}{\bar{x}}\times100=\dfrac{15}{75}\times100=20\%$ .

The coefficient of variation measures relative dispersion:

$C.V.=\frac{\sigma}{\bar{x}}\times100.$

…

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CBSE 2022Set ANNUAL1 markMCQ
$Q. From the following the one which is not the value of a relative measure of dispersion, is :$
(a) ₹ $10$
(b) $0.22$
(c) $0.33$
(d) $0.44$
›Reveal solutionSolution

A relative measure is dimensionless; ₹10 has units ⇒ not relative.

Relative measures of dispersion (coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, coefficient of variation) are formed by dividing one quantity in the same units by another, so the units cancel and the result is a pure number such as $0.22$ , $0.33$ or $0.44$ .

…

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CBSE 2019Set ANNUAL1 mark
$Q. Fill in the blanks:$
(ix) Coefficient of __________ $= \dfrac{\text{Standard Deviation}}{\text{Mean}} \times 100$ .
›Reveal solutionSolution

The blank is Variation.

The coefficient of variation (C.V.) is a relative (unit-free) measure of dispersion defined as

$C.V. = \frac{\sigma}{\bar{x}} \times 100,$ …

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Concept understanding — Coefficient of Variation

Coefficient of Variation

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