There are 7 numbers in both lists so we know that we have not missed any out. It is useful to count the number of data points to check that we have not missed any numbers out. Written from smallest to largest 6, 5, 9, 7, 6, 1, 3 is written as 1, 3, 5, 6, 6, 7, 9. Put the numbers in ascending order from smallest to largest The upper quartile is the median of the second half of the data.įor example, find the five number summary of 6, 5, 9, 7, 6, 1, 3.The lower quartile is the median of the first half of the data.The median is found in the middle of the list.The maximum is the largest number in the list.The minimum is the smallest number in the list.Put the numbers in ascending order from smallest to largest.How to Find the Five Number Summary To find a five number summary: Box plots allow us to compare two sets of data visually. The length of the box itself is longer which indicates a larger interquartile range. The length from whisker to whisker is longer which indicates a larger range. We can see that the box plot of class 2 is longer than the box plot of class 1. The spread is measured using the range and the interquartile range.Ĭlass 2 has a larger range which indicates that the whole data set is more spread than class 1.Ĭlass 2 has a larger interquartile range which indicates that the middle 50% of data in class 2 is more spread out than the middle 50% of data in class 1. We can see that class 2 did better than class 1 on average because class 2 has a larger median. The range and interquartile range are used to compare the spread of data.Īverages are compared on a box plot using the position of the median. The median is used to compare the averages of sets of data. Here is an example of using the 5 number summary to compare two box plots. The interquartile range is 10 and the length of the box portion of the box plot is 10. The upper quartile (Q3) is 20 and the lower quartile (Q1) is 10. The range is 20 and so, the length from whisker to whisker on the box plot is 20. In this example, the maximum is 25 and the minimum is 5. The interquartile range is equal to the length of the box on a box plot. The interquartile range is found using the formula: IQR = Q3 – Q1. The range is the length from whisker to whisker. On a box plot, the range is equal to the length from the first line to the last line. The range is found using the formula: range = maximum – minimum. The median (Q2) is found at the position of the line inside the box at 18.The upper quartile (Q3) is found at the position of the end of the box at 20.The lower quartile (Q1) is found at the position of the start of the box at 10.The maximum is found at the position of the last line at 25.The minimum is found at the position of the first line at 5.Here is an example of reading the 5 number summary from a box plot. The median is found at the line inside the box. The lower quartile is found where the box begins and the upper quartile is found where the box ends. On a box plot, the minimum and maximum are shown by the first and last lines respectively. The 5 number summary consists of the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3) and the maximum. This allows a comparison of ‘typical’ members of a set of data that does not include extreme values. The interquartile range is useful when a comparison of the middle portion of data is required. The interquartile range also describes the spread of the middle 50% data only. However, this means that the range is greatly affected by outliers (extreme results in the data), where the interquartile range is not. The benefit of the range is that it describes the spread of all values in a data set, whereas the interquartile range only considers the middle 50% of data. The range describes the spread of the whole set of data, whilst the interquartile range describes the spread of the middle set of data. The interquartile range = Q3 – Q1 indicates the spread of the middle 50% of the data set.The range = maximum – minimum indicates the spread of the whole data set.The range can be found by subtracting the minimum from the maximum and the interquartile range can be found by subtracting the lower quartile (Q1) from the upper quartile (Q3). The median is the central value which indicates an average point in the data. The five number summary is used to describe a set of data. The upper quartile (Q3) is found three-quarters of the way through the data. The median (Q2) is found after the second quartile, halfway through the data. The lower quartile (Q1) is found after the bottom 25%.
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