Mean, median, mode, range · SAT Maths

Concept

Four basic descriptive statistics:

Mean (average) — sum divided by count. Sensitive to outliers.
Median — the middle value when the data is sorted. If the count is even, average the two middle values. Robust to outliers.
Mode — the most frequently occurring value(s). A dataset may have one mode, several, or none.
Range — max − min. A simple measure of spread.

For a perfectly symmetric distribution with no outliers, mean ≈ median. Right-skewed distributions have mean > median (a long tail on the right pulls the mean up). Left-skewed is the mirror.

Worked example 1

Find the mean, median, and mode of the dataset {2, 5, 5, 8, 10}.

Solution

Mean. (2 + 5 + 5 + 8 + 10) / 5 = 30 / 5 = 6

Median. Sorted: 2, 5, 5, 8, 10. Middle value = 5.

Mode. 5 appears twice — most common ⇒ 5.

Mean 6, median 5, mode 5.

Worked example 2

A class scored {72, 78, 80, 85, 95, 98}. Replace the highest score (98) with 88. Recompute the mean.

Solution

Old sum. 72 + 78 + 80 + 85 + 95 + 98 = 508; old mean ≈ 84.7

New sum. 508 − 98 + 88 = 498

New mean. 498 / 6 = 83

New mean 83. The mean dropped because we removed an extreme high value — proof of how sensitive the mean is to outliers.

Practice test

8 questions on calculating mean, median, mode, range, and recognising outlier effects.

Practice test · 8 questions Question 1 of 8 · Score 0