If mean deviation about median of 12.95 is 54.8, then find the coefficient of mean deviation.

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Q. If mean deviation about median of 12.95 is 54.8, then find the coefficient of mean deviation.

ChseodishaCHSE Odisha Plus Two (Class 12) Commerce Board 2022Subjective· 2mImportance★★★★★est

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Coeff. of M.D. about median $=\dfrac{\text{M.D.}}{\text{Median}}=\dfrac{54.8}{12.95}\approx4.23$ .

The coefficient of mean deviation measured about the median is

$\text{Coeff. of M.D.}=\frac{\text{Mean deviation about median}}{\text{Median}}.$

Taking the stated values — median $=12.95$ and mean deviation about the median $=54.8$ —

$\text{Coeff. of M.D.}=\frac{54.8}{12.95}=4.23\ (\text{approx.}).$

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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.If mean deviation about median of 12.95 is 54.8, then find the coefficient of mean deviation.

Concept understanding — Mean Deviation and its Coefficient

Q.If mean deviation about median of 12.95 is 54.8, then find the coefficient of mean deviation.

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