Q.The marks scored by 8 students in a Business Statistics unit test (out of 50) are: 32, 45, 28, 38, 41, 25, 36, 48. Find the Range and the Coefficient of Range.

Coefficient of range $=\dfrac{L-S}{L+S}=\dfrac{30-5}{30+5}=\dfrac{25}{35}$.

The values are $10, 15, 5, 25, 30$.

Step 1 — identify the largest and smallest:

$L=30,\qquad S=5$

Step 2 — the coefficient of range is

$\dfrac{L-S}{L+S}=\dfrac{30-5}{30+5}=\dfrac{25}{35}$

A measure of dispersion quantifies the scatter of data about a central value.

A measure of dispersion (such as range, quartile deviation, mean deviation or standard deviation) indicates how widely the individual observations are spread out from an average value of the distribution. A small dispersion means the values cluster closely around the average (the average is representative); a large dispersion means they are widely scattered.

Range $= L - S$ (largest minus smallest).

By definition, for a data set with largest value $L$ and smallest value $S$,

$\text{Range} = L - S.$

The coefficient of range $\left(\dfrac{L-S}{L+S}\right)$ is its relative version, but the plain difference itself is simply the range.

Range $=L-S$ uses only extremes, not all data.

The range is computed as $L-S$ (largest minus smallest), so it ignores all the intermediate observations. In contrast:

• Standard deviation uses squared deviations of all values,
• Coefficient of variation is built from the standard deviation and mean of all values,
• Mean deviation averages the absolute deviations of all values.

Hence the range is the measure not based on all the values.

Correct option: (a) Range.

The range is the simplest absolute measure of dispersion, defined as

$\text{Range} = L - S,$

the difference between the largest value $L$ and the smallest value $S$ in the data. Quartile deviation, mean deviation and standard deviation are other measures but none is defined as just the greatest-minus-smallest gap.

Correct option: (a) Range.

Measures of dispersion are of two types: absolute (in the same units as the observations, e.g. range, quartile deviation, mean deviation, standard deviation) and relative (unit-free ratios/percentages used for comparison, e.g. coefficient of range, coefficient of quartile deviation, coefficient of mean deviation, coefficient of variation). Among the options, only range is an absolute measure; the other three are relative measures.