Egypt Primary 6 Mathematics, Week 14: Median and mode: the middle and the most common

Median, mode, outliers and range

Week 14 · Median, mode, outliers and the range · 3 lessons

Median and mode: the middle and the most common

Discover Mathematics P6: Term 1, Unit 7, Lessons 3–4

GoalFind the median and the mode, and say what each one tells us about a typical value.

New words

median · the middle value of the ordered datamode · the value that appears most oftentypical value · one number that describes what is usual in the data

Explanation

A typical value is one number that tells us what is usual in a data set. We already know the mean. The median is the middle value after ordering the data. The mode is the value that appears most often, and we find it by counting. A data set can have two or more modes if several values appear equally often, and it can have no mode at all if every value appears only once. The mode is the only one of the three that also works for words, such as the most popular colour.

★Remember

Median = middle of the ordered data. Mode = most common value (none, one or several). Put the data in order first.

Worked examples

Size	36	37	38	39	40
Pupils	2	4	2	1	1

Shoe sizes of 10 pupils: 36, 37, 37, 38, 37, 39, 38, 37, 40, 36. Counting gives the table. The mode is 37, which appears 4 times. In order: 36, 36, 37, 37, 37, 37, 38, 38, 39, 40. The two middle values are 37 and 37, so the median is 37.

More than one mode, or none. In 2, 3, 3, 5, 5, 7 both 3 and 5 appear twice, so there are two modes, 3 and 5 (the median is (3 + 5) ÷ 2 = 4). In 4, 6, 7, 9 every value appears once, so there is no mode.

Mode for words. A class voted for a colour for the school trip T-shirts: 9 chose blue, 6 green and 5 red. The mode is blue. Here we cannot find a mean or a median, because colours are not numbers; the mode tells us what is most popular.

Class activity

Find the mode at home. Look at the family’s shoes, or the ages of people in your street. Write the data, count how many times each value appears, and say the mode and the median. Is there more than one mode?

Practice

Find the mode and the median of 5, 8, 5, 9, 5, 7, 8.

Find the mode or modes of 1, 2, 2, 3, 3, 4.

Does 1, 2, 3, 4, 5 have a mode?

Find the median and the mode of 13, 7, 9, 7, 11, 7.

The dot plot shows the number of goals scored in 12 matches. Find the mode and the median.