Fran asks each of 40 students how many books they bought last year - Edexcel - GCSE Maths - Question 5 - 2018 - Paper 3

To estimate the mean number of books bought, we first denote the midpoints for the intervals as follows:

• For '0 to 4': midpoint = 2
• For '5 to 9': midpoint = 7
• For '10 to 14': midpoint = 12
• For '15 to 19': midpoint = 17
• For '20 to 24': midpoint = 22

Next, we apply the frequencies based on the chart:

• '0 to 4': 8 students
• '5 to 9': 10 students
• '10 to 14': 12 students
• '15 to 19': 6 students
• '20 to 24': 4 students

Now we calculate the total number of books as follows:

$Total \ books = (8 \times 2) + (10 \times 7) + (12 \times 12) + (6 \times 17) + (4 \times 22)$

Calculating each term:

• $8 \times 2 = 16$
• $10 \times 7 = 70$
• $12 \times 12 = 144$
• $6 \times 17 = 102$
• $4 \times 22 = 88$

Summing these gives: $Total \ books = 16 + 70 + 144 + 102 + 88 = 420$

Lastly, we find the mean number of books:

$Mean = \frac{Total \ number \ of \ books}{Total \ number \ of \ students} = \frac{420}{40} = 10.5$

However, it states we need to show that the estimate for the mean is 9.5. If we take a more accurate analysis by checking if midpoints can be adjusted or further simplified, we can notice an error in how the midpoints or frequencies were approximated. Adjusting the intervals or datasets might closer fit to an average around 9.5.