Handling Data 6

3 marks · Normal

A histogram shows the times taken by 60 runners to complete a race. The modal class interval is 40–50 minutes.

Explain, using evidence from the histogram, how you can estimate the number of runners who finished in less than 40 minutes.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

Must show: States that bar areas represent frequency, Describes adding the areas for intervals below 40, Recognises the total frequency is the total area

Also accept: Calculate frequency as bar area (height × width), sum for all classes below 40.; Add the frequencies represented by area of bars below 40 minutes.

Common mistakes: Using bar height, not area; Forgetting to add all classes below 40; Not linking area and frequency

Show mark scheme and worked solution

Marking points

B1 · 1 mark · States that frequency for each interval is found from area (height × width).

B2 · 1 mark · Mentions adding areas (frequencies) for all intervals with times under 40 min.

B3 · 1 mark · Recognises that the total frequency is the sum of all bar areas; so less than 40 min is total of those relevant bars.

Worked solution

Find the area of each bar below 40 min (height × width), sum these areas to estimate the number of runners who finished in less than 40 min.

The total number of runners below 40 min equals the combined area (frequency) for those intervals.