Measure of spread
Range
The range is one of the ways to measure how spread out the numbers are.
The range is the difference between the highest and lowest numbers.
Here are Kieran's results again:
\(10, 14, 10, 12, 11, 10, 11, 12, 10, 11, 9, 12\)
Kieran's highest number is \(14\) and the lowest \(9\), therefore the range is \(14 - 9 = 5\).
To find the range of a set of numbers, you need to:
- find the lowest number
- find the highest number
- subtract the lowest number from the highest number
- know that the difference between the highest and lowest number is called the range
Question
What is the range of this set of numbers?
\(5, 8, 3, 6, 2, 8, 6, 9, 3\)
Lowest number \(= 2\)
Highest number \(= 9\)
Range \(= 9 - 2 = 7\)
Comparing data
We know that the mean number of tracks on Kieran's albums is 11.
Deepa also counted the number of tracks on her albums and calculated the mean to be 11 as well.
Here are Deepa's results:
\(2, 20, 3, 17, 20, 4, 3, 16, 4, 5, 19, 18, 12\)
She therefore came to the conclusion that her results were very similar to Kieran's but this is not the case.
Here are Kieran's results:
\(10, 14, 10, 12, 11, 10, 11, 12, 10, 11, 9, 12\)
Remember, his range is \(5\).
Although Deepa’s mean is the same as Kieran's mean, the results are very different. Some results are a good bit higher or lower.
The number of tracks on Deepa's albums goes from \(2\) to \(20\).
Range \(= 20 - 2 = 18\)
More information can therefore be shown by giving a measure of spread as well as an average.
