## Exam-Style Question on Statistics## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 715. This question is similar to one that appeared on a GCSE Higher paper in 2022. The use of a calculator is allowed.

(a) The list shows 18 temperatures, in degrees Celsius, at 2pm on different days in Honeyville.

19 | 23 | 23 | 16 | 22 | 18 | 29 | 18 | 23 |

24 | 16 | 23 | 20 | 25 | 23 | 27 | 27 | 23 |

(i) Construct a stem-and-leaf diagram to show this information.

(ii) Find the median.

(iii) Find the lower quartile.

(iv) Graham draws a pie chart to show this information.

Calculate the sector angle for the number of days the temperature is 23°C.

(b) The box-and-whisker plot shows information about the masses, in grams, of some stones.

(i) Find the median.

(ii) Find the range.

(iii) Find the interquartile range.

(c) (i) The time, \( t \) minutes, spent exercising in one week by each of 184 students is recorded. The table shows the results.

$$ \begin{array}{|c|c|} \hline \text{Time } (t \text{ minutes}) & \text{Frequency} \\ \hline 40 < t \leq 60 & 5 \\ 60 < t \leq 80 & 12 \\ 80 < t \leq 90 & 55 \\ 90 < t \leq 100 & 90 \\ 100 < t \leq 150 & 22 \\ \hline \end{array} $$Calculate an estimate of the mean.

(ii) A new table with different class intervals is completed.

$$ \begin{array}{|c|c|} \hline \text{Time } (t \text{ minutes}) & \text{Frequency} \\ \hline 40 < t \leq 90 & 72 \\ 90 < t \leq 150 & 112 \\ \hline \end{array} $$On a histogram the height of the bar for the \( 40 < t \leq 90 \) interval is 7.2 cm.

Calculate the height of the bar for the \( 90 < t \leq 150 \) interval.

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