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Module 1: Range

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Boxplots - example

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Core Mathematics - Boxplots - example

Boxplots - example

Construct a boxplot for the data set 40, 42, 43, 43, 48, 50, 55

X min = 40

Q1 = 42.5

Median = 43

Q3 = 49

IQR = 49 - 42.5 = 6.5

Xmax = 55

Outliers: lower limit: = Q1 - 1.5xIQR

= 42.5 - 1.5x6.5

= 42.5 - 9.75

= 32.75

upper limit = Q3 + 1.5xIQR

= 49 + 1.5x6.5

= 49 + 9.75

= 58.75

All scores lie between 40 and 55, so there are no outliers.

Comments: The median is located near the left end of the box and the left
whisker is far shorter than the right, indicating that the lower scores are
far less spread than the higher scores. This corresponds to a positive
skew.

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