Numeracy Intermediate June 2018 Unit 2 Q12
12. Dr Khan and her daughter Faryl have different opinions about the mean temperature in their hallway.
Dr Khan and Faryl recorded the temperature in the hallway at 4 p.m. each day during the 30 days of April.
In her note pad, Dr Khan summarised the temperatures in a grouped frequency table.
Unfortunately, Dr Khan has torn the page containing the table from her note pad and has lost some of the original data.
Calculate an estimate of the mean temperature at 4 p.m. for these 30 days in Dr Khan’s hallway. [5]
Estimate of the mean temperature at 4 p.m. for April in the hallway is …………… °C
What assumption have you made in calculating an estimate of the mean temperature at 4 p.m. for April in Dr Khan’s hallway? [1]
Faryl recorded the same temperatures as her mother at 4 p.m. each day during April.
She found that the actual mean temperature in the hallway during April was lower than the correctly calculated estimate of the mean.
Explain how this can be true. [1]
| Scheme | Marks | Comments |
|---|---|---|
| Midpoints 20.5, 21.5, 22.5, 23.5 | B1 | |
| Missing 10 days for 23 ≤ t < 24 | B1 | |
| 20.5×4+21.5×8+22.5×8+23.5×10 (= 82 + 172 + 180 + 235 = 669) | M1 | FT ‘their 10’ provided ≠0 Allow with incorrect midpoints provided each one is within the correct interval including ‘bounds’ |
| ÷ 30 | m1 | FT 20 + ‘their 10’ |
| 22.3(°C) | A1 | Allow 22(°C) from correct working If no marks or first B1 only, award SC1 for an answer of 21.7 (°C) (from working with the 20 days given) |
| Scheme | Marks | Comments |
|---|---|---|
| Suitable assumption stated, e.g. ‘used the midpoints (to represent each group)’, ‘I used a value in each of the groups to represent the group’, ‘the temperature is between the 2 values each time’ | E1 | FT from 'their points' used in (a) |
| Scheme | Marks | Comments |
|---|---|---|
| Suitable reason given, e.g. ‘many of the temperatures were less than the midpoint of the group in which they were recorded’, ‘the temperatures were often towards the lower end of the groups’ | E1 | Do not accept e.g. ‘mid points were used’, 'Faryl used exact values', 'raw data was used by Faryl', 'Faryl found the actual mean' without further explanation |