The histogram in Figure 1 shows the time taken, to the nearest minute, for 140 runners to complete a fun run - Edexcel - A-Level Maths Statistics - Question 3 - 2008 - Paper 1

To find the number of runners who took between 78.5 and 90.5 minutes, we first determine the area under the histogram between these two time marks. The appropriate bars in the histogram are:

• The bar for 78 to 80 minutes has a height of 6.
• The bar for 80 to 82 minutes has a height of 4.
• The bar for 82 to 84 minutes has a height of 2.
• The bar for 84 to 86 minutes has a height of 1.
• The bar for 86 to 88 minutes has a height of 0.
• The bar for 88 to 90 minutes has a height of 1.

The width of each interval that we're interested in is 2 minutes (except for the last bar which is from 88 to 90).

Thus, the area is calculated as follows:

• For the bar 78-80: Area = Width × Height = 2 × 6 = 12
• For the bar 80-82: Area = 2 × 4 = 8
• For the bar 82-84: Area = 2 × 2 = 4
• For the bar 84-86: Area = 2 × 1 = 2
• For the bar 86-88: Area = 2 × 0 = 0
• For the bar 88-90: Area = 2 × 1 = 2

Adding these areas gives: $ext{Total Area} = 12 + 8 + 4 + 2 + 0 + 2 = 28$

This area represents the total number of runners in that range out of the total 140 runners.