Write the two formulae for determining the relative measure of mean deviation about mean and about median.

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Q. Write the two formulae for determining the relative measure of mean deviation about mean and about median.

ChseodishaCHSE Odisha Plus Two (Class 12) Commerce Board 2024Subjective· 2mImportance★★★★★est

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Coefficient of M.D. $=\dfrac{\text{mean deviation}}{\text{average used}}$ .

The relative measure of mean deviation (a unit-free ratio used for comparison) is obtained by dividing the mean deviation by the average about which it is computed:

$\text{Coefficient of M.D. about mean}=\frac{M.D._{\bar{x}}}{\bar{x}},$ …

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

CBSE 2022Set ANNUAL1 markMCQ
$Q. From the following the one which is a relative measure of dispersion is :$
(a) Range
(b) Quartile deviation
(c) Coefficient of mean deviation
(d) Standard deviation
›Reveal solutionSolution
Relative measures are ratios/coefficients; here that is the coefficient of mean deviation.

Measures of dispersion are of two kinds:

Absolute — expressed in the original units (Range, Quartile deviation, Mean deviation, Standard deviation).

Relative — a unit-free ratio obtained by dividing an absolute measure by an average (Coefficient of range, Coefficient of quartile deviation, Coefficient of mean deviation, Coefficient of variation). …
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CBSE 2022Set ANNUAL1 markMCQ
$Q. The mean deviation of 10, 12, 20 and 30, is :$
(a) $7$
(b) $18$
(c) $14$
(d) $6$
›Reveal solutionSolution

$\bar{x}=18$ , $\text{M.D.}=\frac{8+6+2+12}{4}=7$ .

Mean:

$\bar{x}=\frac{10+12+20+30}{4}=\frac{72}{4}=18.$

Absolute deviations from the mean:

$|10-18|=8,\;|12-18|=6,\;|20-18|=2,\;|30-18|=12.$

…

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CBSE 2022Set ANNUAL1 markMCQ
$Q. The formula for calculating coefficient of mean deviation is :$
(a) $\frac{\text{Mean}}{\text{Mean deviation}}$
(b) $\frac{\text{Mean deviation}}{\text{Mean}}$
(c) $\text{Mean deviation} \times \text{Mean}$
(d) $\frac{\text{Median}}{\text{Mean deviation}}$
›Reveal solutionSolution

Coefficient of M.D. $=\dfrac{\text{Mean deviation}}{\text{average used}}$ .

A relative measure of dispersion is formed by dividing the absolute measure by the corresponding average. For mean deviation taken about the mean,

$\text{Coefficient of M.D.}=\frac{\text{Mean deviation}}{\text{Mean}}.$

…

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Q.Write the two formulae for determining the relative measure of mean deviation about mean and about median.

Concept understanding — Mean Deviation and its Coefficient

Q.Write the two formulae for determining the relative measure of mean deviation about mean and about median.

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