Statistics Fundamentals • Topic 2 of 6

Median

The median is the middle value once the data is put in order. For an odd number of values it is the single middle one; for an even number it is the mean of the two middle values. Because it depends only on position, the median is resistant to outliers — extreme values barely move it, unlike the mean. Always sort first; forgetting to order the list is the classic error. On the SAT the median is favoured for skewed data, and questions often compare how the mean and median respond to an extreme value.

✅ Solved examples

1. Find the median of 3, 5, 1, 4, 2.
Sorted: 1, 2, 3, 4, 5; the middle value is 3.
2. Find the median of 2, 4, 6, 8.
Even count: mean of the two middle values (4 and 6) = 5.
3. Find the median of 10, 2, 8, 4, 6, 12.
Sorted: 2,4,6,8,10,12; middle two are 6 and 8; median = 7.
4. A set of 9 numbers has median 15. The largest is increased. New median?
The middle position is unchanged, so the median stays 15.

✏️ Practice — try these, take hints as needed

1. Find the median of 7, 3, 9, 5, 1.
Sort the values.
1, 3, 5, 7, 9.
Middle value.
5.
2. Find the median of 4, 8, 10, 14.
Even count.
Average the two middle values (8 and 10).
—
9.
3. Find the median of 12, 4, 6, 2, 10, 8.
Sort: 2,4,6,8,10,12.
Average the middle two.
(6 + 8)/2.
7.
4. Find the median of 5, 5, 9, 11.
Already ordered.
Average 5 and 9.
—
7.
5. A set of 7 numbers has median 20. The smallest decreases. New median?
Order of the middle value is unchanged.
Median position fixed.
—
20.

📝 Topic test — 8 questions

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