Median

## Median

The Median is the middle value of a set of data, when the data is sorted in order.

The middle item can be calculated as frac(n+1)(2), where n is the number of items.

Where there is an even number of items, then the calculation gives a frac(1)(2) as a remainder. In this instance, add the two numbers on either side of the halfway mark and divide by 2.

A median can be used to describe a population where there is a range of specific values. Medians are not heavily influenced by outliers.

## Example 1

Ten piles of coins are placed on a table. The number of coins in each pile is 3, 5, 1, 6, 7, 3, 5, 4, 2, 4. What is the median number of coins in a pile?

Place the values in order: 1, 2, 3, 3, 4, 4, 5, 5, 6, 7

The median is the frac((10+1))(2) = 5frac(1)(2) value.

The value is between the 5th and 6th piles, which have values 4 and 4. The median is 4.

## Example 2

A supermarket samples the number of strawberries in trays. From 10 trays, the numbers of strawberries obtained was 12, 14, 13, 16, 11, 12, 15, 16, 14, 13. What was the median number of strawberries in each tray?

Put the trays in order of the number of strawberries.

11, 12, 12, 13, 13, 14, 14, 15, 16, 16

The median position is frac(10 + 1)(2) = 5.5, so the 5th and 6th position.

The 5th tray has 13 strawberries, the 6th tray has 14 strawberries.

(13 + 14) ÷ 2 = 13.5