Median, Quartiles, Inter-Quartile Range
Remember: The range is the measure of spread that goes with the mean.
Example 1. Two dice were thrown 10 times and their scores were added together and recorded. Find the mean and range for this data.
7, 5, 2, 7, 6, 12, 10, 4, 8, 9
Mean = 7 + 5 + 2 + 7 + 6 + 12 + 10 + 4 + 8 + 9/10=70/10
7
Range = 12 – 2 = 10
The range is not a good measure of spread because one extreme, (very high or very low value) can have a big affect. The measure of spread that goes with the median is called the inter-quartile range and is generally a better measure of spread because it is not affected by extreme values.
Averages (The Median)
The median is the middle value of a set of data once the data has been ordered.
Example 1. Robert hit 11 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives.
85, 125, 130, 65, 100, 70, 75, 50, 140, 95, 70
50, 65, 70, 70, 75, 85, 95, 100, 125, 130, 140
The median is 85 as if you count the amount of numbers and divide by 2 you get 5.5 rounded which is 6 and the 6th number is 85. If there are 2 numbers in the middle add them and divide by 2 to get your answer.
Finding the median, quartiles and inter-quartile range.
Example 2: Find the median and quartiles for the data below.
6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10
Order the data
Q1 Q2 Q3
3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15,
Lower Quartile = 4 Median = 8 Upper Quartile = 10
Inter-Quartile Range = 10 - 4 = 6