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If you place a set of numbers in order, the median number is the middle one.
If there are two middle numbers, the median is the mean of those two numbers.
Find the median of each of the following sets of numbers:
a) 2, 4, 7, 1, 9, 3, 11
b) 4, 1, 3, 10, 6, 9,
a) Place the numbers in order:
1, 2, 3, 4, 7, 9, 11
The middle number is 4. Therefore the median is 4.
b) Place the numbers in order:
1, 3, 4, 6, 9, 10
there are two middle numbers (4 and 6), so we find the mean of these two numbers. The median is therefore:
(4 + 6) ÷ 2 = 5
In general:
If there are n numbers, the median will be the (n + 1) ÷ 2 = th number
If there are 3 numbers, the median will be the (3 + 1) ÷ 2 = 2nd number.
If there are 4 numbers, the median will be the (4 + 1) ÷ 2 = 2^{1}/_{2}^{th} number
Rachel records the number of goals scored by her five-a-side team in their first 20 matches.
The results are shown in the frequency table below:
Numbers of goals | Frequency |
---|---|
0 | 7 |
1 | 5 |
2 | 6 |
3 | 0 |
4 | 2 |
4 | 0 |
What is the median number of goals scored?
20 matches were played, so the median will be the 21 ÷ 2 ^{th} value.
7 matches scored 0 goals, and 5 matches scored 1 goal.
The 21 ÷ 2 ^{th} value lies in the '1 goal' category.
21 ÷ 2 = 10 ^{1}/_{2}
Therefore, the median number of goals is 1.
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