Numeracy Higher November 2017 Unit 1 Q3
3.
No job too small!
Email: meirion@mwcb.cymru
Meirion is a window cleaner.
From Monday to Friday, he records how long he spends cleaning windows for each of his customers.
He draws a cumulative frequency diagram to display the findings.
Use Meirion’s cumulative frequency diagram to find the median and interquartile range of the times he spends cleaning windows for each of his customers. [3]
Median …………… minutes
Interquartile range …………… minutes
Meirion looks back at his raw data.
He finds that the median is actually 17 minutes 30 seconds.
Why is there a difference between the median from his cumulative frequency diagram and the actual median from his raw data? [1]
Meirion is looking at the time it took to clean individual customers’ windows.
Find the number of customers whose windows took between 10 and 15 minutes to clean. [2]
Meirion thinks that for approximately 80% of his customers, he cleaned their windows in less than 20 minutes.
Is Meirion correct?
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (i) Median in the inclusive range 16.8 to 17 (minutes) | B1 | |
| Interquartile range 19 to 19.3 - 14 to 14.3 | M1 | |
| Answer in the range 4.7 to 5.3 (minutes) | A1 | |
| (ii) Reason, e.g. ‘the points on the diagram have been joined with straight lines’, ‘the data has been grouped, so actual times have been lost’, ‘the raw data is more detailed (than graph)’, ‘not exact using a cumulative frequency diagram’, ‘it is just an estimate using the diagram’ | E1 | Allow, e.g. ‘the raw data is more detailed than Meirion’s data’ (although both Meiron’s data!), ‘the points could be joined by a curve’ Do not accept, e.g. ‘seconds can not be presented’ |
| Scheme | Marks | Comments |
|---|---|---|
| 34 – 12 | M1 | |
| 22 (of his customers) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
Sight of either of the following:
| M1 | Accept readings on the graph |
Sight of any of the following:
| M1 | Accept readings on the graph |
| Conclusion ‘yes’ | A1 | CAO from correct working only and M2 awarded Accept ‘no as 85% (not 80%) in less than 20 minutes’ |