The 5 - number summary of the distribution obtained from the boxplot is :
- Minimum = 20
- Maximum = 85
- Lower quartile = 35
- Median = 44
- Upper quartile = 58
- Outlier = 100
Firstly, we need to extract the values for the amount spent by females :
20, 25, 25, 35, 37, 38, 39, 43, 45, 46, 50, 53, 60, 70, 85, 100
The five number summary include ;
- Minimum, lower Quartile, Median, Upper Quartile and Maximum values.
Rearranging the data in ascending order :
20, 25, 25, 35, 37, 38, 39, 43, 45, 46, 50, 53, 60, 70, 85, 100
The boxplot clearly and easily gives the five number summary of the distribution :
- Minimum = 20 (starting point of the whisker)
- Lower quartile = 35 (starting point of the box)
- Median = 44 (vertical line in between the box)
- Upper quartile = 58 (endpoint of the box)
- Maximum = 85 (endpoint of the upper whisker).
Outlier :
- Lower boundary = LOWER QUARTILE - (1.5 × IQR)
- Upper boundary = UPPER QUARTILE + (1.5 × IQR)
- IQR = UPPER QUARTILE - LOWER QUARTILE
- IQR = (58 - 35) = 23
Lower boundary = 35 - (1.5 × 23) = 0.5
Upper boundary = 58 + (1.5 × 23) = 92.5
- The point denoted by a dot on the boxplot is an outlier = 100
Hence, values lesser than 0.5 or greater than 92.5 are outliers.
Therefore, 100 is an outlier.
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