Which of the following is a measure of dispersion?

Step 1: Analyze the question We are asked which option measures dispersion, meaning how spread out the data values are.

Step 2: Explain the concept In statistics there are two main kinds of measures:

• Measures of central tendency show the "centre" or typical value of the data: mean, median, mode.
• Measures of dispersion (spread) show how scattered the data are: range, variance, standard deviation, mean deviation, and interquartile range (and semi-interquartile range).

Step 3: Check each option

• A. Range: Highest value − lowest value. It directly shows how spread out the data are, so it is a measure of dispersion.
• B. Percentile: A measure of position (the value below which a given percentage of the data falls). It is not a spread measure by itself.
• C. Median: The middle value, so it is a measure of central tendency.
• D. Quartile: Also a measure of position (it divides data into four parts). Only the difference between quartiles (the interquartile range, Q₃ − Q₁) measures dispersion, not a quartile alone.

Step 4: Answer The range is the only option that is itself a measure of dispersion.

Example: for the data 3, 5, 8, 12, the range = 12 − 3 = 9, which tells us how widely the numbers are spread.

Exam tip: Remember "Range, Variance, Standard deviation" as the spread family. Mean, median and mode are the "centre" family. Quartiles and percentiles show position; they only describe spread when you subtract them (like Q₃ − Q₁).