Identify the measures of dispersion : (A) Mean deviation (B) Median (C)…

Descriptive statistics group measures into three families: measures of central tendency (mean, median, mode) locate the centre of a data set; measures of dispersion (or variability) quantify how spread out the values are around that centre; and positional/location measures (quartiles, deciles, percentiles) mark specific ranks in the ordered data without themselves quantifying spread.

Classifying each item in the list:

• Mean deviation — the average of the absolute deviations of each value from the mean; a measure of dispersion.

• Median — the middle value of the ordered data; a measure of central tendency.

• Standard deviation — the square root of the average of the squares of the deviations from the mean; the most widely used measure of dispersion.

• Range — the difference between the maximum and minimum values; the simplest measure of dispersion.

• Quartile — a positional value that divides the ordered data into four equal parts; a measure of location, not dispersion itself (the quartile deviation derived from the quartiles is a dispersion measure, but a quartile itself is not).

Contrasting the two items that do not qualify:

• Median is excluded — it locates the centre of the data, so it is a measure of central tendency, not dispersion.

• Quartile is excluded — it marks a rank within the ordered data, so it is a positional/location measure, not a measure of dispersion.

Mean deviation, standard deviation, and range are the three items that directly quantify spread. Hence the correct selection is (A), (C) and (D) only.