| Date | May 2022 | Marks available | 3 | Reference code | 22M.1.SL.TZ1.3 |
| Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 1 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
A survey at a swimming pool is given to one adult in each family. The age of the adult, years old, and of their eldest child, years old, are recorded.
The ages of the eldest child are summarized in the following box and whisker diagram.
The regression line of on is . The regression line of on is .
Find the largest value of that would not be considered an outlier.
One of the adults surveyed is years old. Estimate the age of their eldest child.
Find the mean age of all the adults surveyed.
Markscheme
(A1)
attempt to find (M1)
A1
[3 marks]
choosing (M1)
(years old) A1
[2 marks]
attempt to solve system by substitution or elimination (M1)
(years old) A1
[2 marks]
Examiners report
Many candidates correctly found the value of 16. Some then incorrectly went on to state that 15 was therefore the minimum value that was not an outlier. For part (b) students needed to choose the appropriate rule to use to estimate the child's age. It was clear that many did not know there was a choice to be made and used both equations. As the mean point (𝑐̅,𝑎̅ ) lies on both regression lines, in part (c) candidates needed to solve the system of equations to find the mean adult age, 𝑎̅. Few candidates seemed to be aware of this.
