There are two companies U and V which manufacture cars. A sample of 40 cars each from these companies are take

Miscellaneous Exercise 8 (II) · Q54

There are two companies U and V which manufacture cars. A sample of 40 cars each from these companies are taken and the average running life (in years) is recorded.

Life (in years)	Company U	Company V
0-5	5	14
5-10	18	8
10-15	17	18

Which company shows greater consistency?

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Step 1 — Company U: mid-values 2.5, 7.5, 12.5 with frequencies 5, 18, 17 ( $N=40$ ). $\sum f_ix_i = 12.5+135+212.5=360$ , mean $=360/40=9$ . $\sum f_ix_i^2 = 31.25+1012.5+2656.25=3700$ . $\text{Var}=3700/40-81=92.5-81=11.5$ , so $\sigma_U\approx3.39$ .

Step 2: $\text{C.V.}_U = 100\times3.39/9\approx37.68\%$ .

Step 3 — Company V: same mid-values with frequencies 14, 8, 18 ( $N=40$ ). $\sum f_ix_i = 35+60+225=320$ , mean $=320/40=8$ . $\sum f_ix_i^2 = 87.5+450+2812.5=3350$ . $\text{Var}=3350/40-64=83.75-64=19.75$ , so $\sigma_V\approx4.44$ . …

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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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