Foundation November 2024 Paper 3 Q15
15 The table gives information about the ages of the 41 children in Blackrod football club.
| Age (years) | Frequency |
|---|---|
| 8 | 6 |
| 9 | 7 |
| 10 | 15 |
| 11 | 11 |
| 12 | 2 |
(a) Work out the mean age.
Give your answer correct to 1 decimal place. (3)
Give your answer correct to 1 decimal place. (3)
Rohan is working out the modal age of the children in Blackrod football club.
He says,
“The highest frequency is 15, so the modal age is 15”
(b) Is Rohan’s answer correct?
Give a reason for your answer. (1)
Give a reason for your answer. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 9.9 | M1 | for starting process by multiplying ages by frequencies, with at least 3 correct, eg \(8 \times 6\), \(9 \times 7\), \(10 \times 15\), \(11 \times 11\), \(12 \times 2\) or at least 3 of 48, 63, 150, 121, 24 |
| M1 | (dep on M1) for \(\sum fx \div \sum f\), eg \(406 \div 41\) or \(406 \div (6 + 7 + 15 + 11 + 2)\) or \((8 \times 6 + 9 \times 7 + 10 \times 15 + 11 \times 11 + 12 \times 2) \div 41\) | |
| A1 | Answer in the range 9.9 to 9.91 |
Additional guidance
May be seen next to table.
406 implies this mark
\(\sum fx\) must come from 5 products
If an answer is given in the range in working and then rounded incorrectly award full marks.
| Answer | Mark | Mark scheme |
|---|---|---|
| No, with explanation | C1 | No, with explanation, Acceptable examples No as the mode/modal age is 10 No it should be 10 (not 15) No because 15 is the number of children that are age 10 (not age 15) No because there are no 15 year olds No because the frequency tells us the number of children for that age No he needs to give the age of the highest frequency Not acceptable examples No he is not, the modal is the one that occurs the most Yes / Rohan is correct .... No, the mode is 11 |