The histogram summarises a health score for a group of people - OCR - GCSE Maths - Question 10 - 2017 - Paper 1

To estimate the fraction of the group who had a score of 45 or more, observe the histogram. We need to find the area of the bars corresponding to scores of 45 and above.

1. Identify the relevant range: The scores of 45-100 correspond to the histogram bars that start at 40 and end at 100.

2. Estimate the height of the bars: From the histogram, the height at 40-50 is approximately 0.5, and from 50-60, it is approximately 0.9, with decreasing values for the remaining intervals.

3. Calculate the area under these bars:

   • For the 40-50 interval (height 0.5 and width 10):

     $ext{Area} = ext{Height} \times \text{Width} = 0.5 \times 10 = 5$

   • For the 50-60 interval (height 0.9 and width 10):

     $ext{Area} = 0.9 \times 10 = 9$

   • For the 60-70 interval (height 0.4 and width 10):

     $ext{Area} = 0.4 \times 10 = 4$

   • For the 70-80 interval (height 0.2 and width 10):

     $ext{Area} = 0.2 \times 10 = 2$

   • For the 80-90 interval (height 0.1 and width 10):

     $ext{Area} = 0.1 \times 10 = 1$

4. Sum the areas:

   $ext{Total Area} = 5 + 9 + 4 + 2 + 1 = 21$

5. Estimate the total number of participants from the histogram, if treated as 100:

   $ext{Fraction} = \frac{21}{100} = 0.21$

Therefore, the estimated fraction of the group who had a score of 45 or more is approximately 0.21.