Median

Median

GCSE(F),

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

The middle term can be calculated as `frac((n + 1))(2)`

Where there is an even number of terms, 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.

Examples

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?

Answer: 4

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

The median is the `frac((10+1))(2)` = 5`frac(1)(2)` the value The halfway value is between the 5th and 6th piles, with values 4 and 4. The median is 4.

2. A stem-and-leaf diagram showed the number of strawberries in trays from a local supermarket. What is the median number of strawberries in each tray?

Answer: There are 15 trays

The median tray is `frac((15+1))(2)` = 8 trays.

Counting in 8 from the stem-and-leaf diagram = 2|3 = 23 strawberries.