Business Mathematics and Statistics · Ch 8 — Measures of Central Tendency
Merits, Limitations and Choice of an Appropriate Average
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Merits, Limitations and Choice of an Appropriate Average
Every average studied in this chapter trades off some of the six requisites of §1 against the others. The table below brings the comparison together.
| Average | Merits | Limitations | Best suited for |
|---|---|---|---|
| Arithmetic Mean | Rigidly defined; based on every observation; capable of further algebraic treatment (combined/weighted mean, §4); least affected by sampling fluctuation | Unduly affected by extreme values; needs an estimate for open-ended classes; can be a figure no single observation actually takes | Fairly symmetric data with no extreme outliers; general-purpose business reporting |
| Median | Not affected by extreme values; can be located even with open-ended classes; can be found graphically via the ogive (§7) | Not based on all observations (ignores the actual magnitude of values on either side); cannot be combined algebraically like the mean; needs the data arranged in order | Income, wage and other markedly skewed distributions |
| Mode | Not affected by extreme values; easy to understand as the "most typical" value; useful for demand-style data | Often ill-defined (no mode, or more than one); not based on all observations; cannot be combined algebraically | Data where the single most frequently occurring value is the figure of real interest — fashion sizes, most-demanded product variant |
| Geometric Mean | Based on all observations; capable of further algebraic treatment; less disturbed by extreme values than the arithmetic mean; the mathematically correct average for rates of growth | Difficult to compute and understand without logarithms; undefined if any value is zero or negative | Growth rates, compound interest, index numbers |
| Harmonic Mean | Based on all observations; the mathematically correct average for rates expressed per unit of time or another base quantity | Difficult to compute and understand; gives disproportionate weight to small values; undefined if any value is zero | Average speed; average price paid per unit of expenditure |