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Box plots

Box plots

A Box Plot gives a visual presentation of the median and spread of a set of data. The Box Plot shows the Range, Inter-Quartile Range and the Mean.

It is also known as a Box and Whisker Diagram.

The diagram consists of 5 pieces of information. The Lowest Value is taken from the lowest value in the data set; similarly the Highest Value. The Median is the middle value when placed in order; the Lower Quartile is the `frac((n + 1))(4)`th value (reading from the lowest value) and the Upper Quartile is the `frac(3(n + 1))(4)`th value (also when reading from the lowest value).

Names of parts of a box and whisker diagram

A Box plot can also be drawn from a Cumulative Frequency diagram.

Cumulative frequency diagram with box-and-whisker

Box Plots give more information on the spread of data, which is useful when comparing sets of data:

• a compact box, with long whiskers, shows the probable presence of outliers;

• a compact box, with short whiskers, shows a consistent set of data;

• an extended box, with long whiskers, shows a wide range of inconsistent data;

• an extended box, with short whiskers, shows a consistent set of data over a wide range.

Example 1

Draw a Box plot for the following information, which is the speed of 27 cars through a radar trap in a 40mph zone:

34, 36, 37, 37, 33, 42, 44, 35, 46, 33, 38, 39, 40, 41, 20, 44, 38, 37, 42, 36, 41, 40, 40, 39, 40, 39, 39

Sort the data into order: a Stem-and-Leaf diagram could be used:

2 0
3 3 3 4 5 6 6 7 7 7 8 8 9 9 9 9
4 0 0 0 0 1 1 2 2 4 4 6

Key 2|0 represents 20mph

Lowest Value is 20

Highest Value is 46

Median Value is the 13th value, which is 39

Lower Quartile is `frac((27+1))(4)` = 7th car = 36

Upper Quartile is 3`frac(27+1)(4)` = 21st car = 41

Answer: Drawn box and whisker diagram

Example 2

Two classes were each given a test paper. The information was shown on a box plot. Make two comparisons between the results from class A and the results from class B.

Comparison of two box and whisker diagrams

Use a comparison of both the average and the range.

Answer: Class B had a higher median score.

Class B also had a smaller interquartile range.

See also Median and Quartiles