The following are measures of location except________

Analyze the question: You are asked to find the one option that is NOT a measure of location. In statistics (which is part of the JAMB Economics syllabus), the word "except" means three options belong to the group and one does not.

Explain the concept:

Statistical measures fall into two main groups:

1. Measures of location (central tendency): These show where the centre or typical value of the data lies. Examples are: • Arithmetic mean • Geometric mean • Harmonic mean • Median • Mode

2. Measures of dispersion (spread): These show how scattered the data is. Examples are: • Range • Variance • Standard deviation • Mean deviation • Quartile (interquartile) range

Solution, option by option:

• A. Arithmetic mean: the sum of values divided by the number of values. It is a measure of location. ✔
• B. Harmonic mean: the reciprocal of the mean of reciprocals. It is a measure of location. ✔
• C. Range: the highest value minus the lowest value. It tells you how spread out the data is, not where the centre is. It is a measure of dispersion, so it is the odd one out. ✘
• D. Geometric mean: the nth root of the product of n values. It is a measure of location. ✔

Answer: The range is the only measure of dispersion in the list, so it is the exception.

Exam tip: Remember the three "M"s plus the other means: Mean, Median, Mode (and Geometric/Harmonic means) tell you the centre. Anything that talks about spread, such as range, variance, standard deviation, is dispersion. Whenever "range" shows up in a "measures of location" question, it is almost always the exception.