Draw box plot from summary statistics

2 A group of children played a computer game which measured their time in seconds to perform a certain task. A summary of the times taken by girls and boys in the group is shown below.

1. On graph paper, draw two box-and-whisker plots in a single diagram to illustrate the times taken by girls and boys to perform this task.
2. State two comparisons of the times taken by girls and boys.

4 The marks of the pupils in a certain class in a History examination are as follows. $$\begin{array} { l l l l l l l l l l l l l } 28 & 33 & 55 & 38 & 42 & 39 & 27 & 48 & 51 & 37 & 57 & 49 & 33 \end{array}$$ The marks of the pupils in a Physics examination are summarised as follows.
Lower quartile: 28 , Median: 39, Upper quartile: 67.
The lowest mark was 17 and the highest mark was 74 .

1. Draw box-and-whisker plots in a single diagram on graph paper to illustrate the marks for History and Physics.
2. State one difference, which can be seen from the diagram, between the marks for History and Physics.

1. A coach recorded the heights of some adult rugby players and found the following summary statistics.

$$\begin{array} { r } \text { Median } = 1.85 \mathrm {~m}
\text { Range } = 0.28 \mathrm {~m}
\text { Interquartile range } = 0.11 \mathrm {~m} \end{array}$$ The coach also noticed that

• the height of the shortest player is 1.72 m
• \(25 \%\) of the players' heights are below the height of a player whose height is 1.81 m

Draw a box and whisker plot to represent this information on the grid below.
\includegraphics[max width=\textwidth, alt={}, center]{6a0b46f8-7a6a-4ed8-8c7a-9772787f155a-02_342_1096_1027_488}

1. The students in a class were each asked to write down how many CDs they owned. The student with the least number of CDs had 14 and all but one of the others owned 60 or fewer. The remaining student owned 65 . The quartiles for the class were 30,34 and 42 respectively.

Outliers are defined to be any values outside the limits of \(1.5 \left( \mathrm { Q } _ { 3 } - \mathrm { Q } _ { 1 } \right)\) below the lower quartile or above the upper quartile. On graph paper draw a box plot to represent these data, indicating clearly any outliers.
marks)

4. Aeroplanes fly from City \(A\) to City \(B\). Over a long period of time the number of minutes delay in take-off from City \(A\) was recorded. The minimum delay was 5 minutes and the maximum delay was 63 minutes. A quarter of all delays were at most 12 minutes, half were at most 17 minutes and \(75 \%\) were at most 28 minutes. Only one of the delays was longer than 45 minutes. An outlier is an observation that falls either \(1.5 \times\) (interquartile range) above the upper quartile or \(1.5 \times\) (interquartile range) below the lower quartile.

1. On the graph paper opposite draw a box plot to represent these data.
2. Comment on the distribution of delays. Justify your answer.
3. Suggest how the distribution might be interpreted by a passenger who frequently flies from City \(A\) to City \(B\).
   \includegraphics[max width=\textwidth, alt={}, center]{9698650f-ef85-468d-a703-1b40df7f9d02-07_1190_1487_278_223}

1. The students in a class were each asked to write down how many CDs they owned. The student with the least number of CDs had 14 and all but one of the others owned 60 or fewer. The remaining student owned 65 . The quartiles for the class were 30,34 and 42 respectively.

Outliers are defined to be any values outside the limits of \(1.5 \left( Q _ { 3 } - Q _ { 1 } \right)\) below the lower quartile or above the upper quartile. On graph paper draw a box plot to represent these data, indicating clearly any outliers.
(7 marks)

4. Aeroplanes fly from City \(A\) to City \(B\). Over a long period of time the number of minutes delay in take-off from City \(A\) was recorded. The minimum delay was 5 minutes and the maximum delay was 63 minutes. A quarter of all delays were at most 12 minutes, half were at most 17 minutes and \(75 \%\) were at most 28 minutes. Only one of the delays was longer than 45 minutes. An outlier is an observation that falls either \(1.5 \times\) (interquartile range) above the upper quartile or \(1.5 \times\) (interquartile range) below the lower quartile.

1. On the graph paper opposite draw a box plot to represent these data.
2. Comment on the distribution of delays. Justify your answer.
3. Suggest how the distribution might be interpreted by a passenger who frequently flies from City \(A\) to City \(B\).
   \includegraphics[max width=\textwidth, alt={}, center]{3d4f7bfb-b235-418a-9411-a4d0b3188254-008_1190_1487_278_223}