Box Plots and 5-Number Summary, SM-Bank 014

The test results in English and Mathematics for a class were recorded and displayed in the box plots.

What is the interquartile range for English? (1 mark)

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Compare and contrast the two data sets by referring to the skewness of the distributions and the measures of their centres and spread. (3 marks)

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Show Answers Only

i. `text{IQR}_text{(English)}\ = 80-50=30`

ii. `text(Skewness)`

`text(English has greater negative skew)`
`text(Maths is more normally distributed)`

`text(Location and Spread)`

`text(English has a range of 85, Maths has 40.)`
`text{English has larger IQR than Maths (30 vs 15)}`
`text{Maths’ median (75) is higher than English (70)}`
`text{Same upper quartile marks (80)}`
`text(English has highest and lowest individual mark)`

Show Worked Solution

i. `text{IQR}_text{(English)}\ = 80-50=30`

♦ Mean mark (ii) 35%
COMMENT: The best answers use the correct language of location and spread such as mean, median, interquartile range, standard deviation and skewness.

ii. `text(Skewness)`

`text(English has greater negative skew)`
`text(Maths is more normally distributed)`

`text(Location and Spread)`

`text(English has a range of 85, Maths has 40.)`
`text{English has larger IQR than Maths (30 vs 15)}`
`text{Maths’ median (75) is higher than English (70)}`
`text{Same upper quartile marks (80)}`
`text(English has highest and lowest individual mark)`