Numeracy Higher June 2018 Unit 1 Q7
7. There are two entrances to a stadium, North Entrance and South Entrance.
At each entrance, 3000 people queued to pass through security.
The length of time each of these people spent in the queue was recorded.
The box-and-whisker diagrams show the results.
(a) At the North Entrance, how many people had to queue for more than 44 minutes?
You must show all your working. [2]
You must show all your working. [2]
Number of people is ……………………
(b) For the South Entrance, calculate an estimate of the number of people who had to queue there for between 40 and 60 minutes.
You must show all your working. [3]
You must show all your working. [3]
Number of people is ……………………
(c) At which entrance did the security team seem to be more effective at getting people into the stadium quickly?
You must give a reason for your answer. [1]
You must give a reason for your answer. [1]
North Entrance ☐ South Entrance ☐
| Scheme | Marks | Comments |
|---|---|---|
| 25% of 3000 or 0.25 × 3000 or equivalent | M1 | |
| 750 (people) | A1 | If no marks, award SC1 for an answer of 2250 (people) |
| Scheme | Marks | Comments |
|---|---|---|
| Idea to consider fraction or decimal part between the median & UQ | M1 | For example, sight of 10/15 (= ⅔) or 5/15 (= ⅓) |
| ⅔ × 0.25 × 3000 or equivalent | m1 | FT 'their 750' from (a)' |
| 500 (people) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| Do not ignore additional incorrect statements | ||
| Indicates or unambiguously implies ‘North Entrance’ with a suitable reason, e.g. ‘upper quartile is less than for the South Entrance’, ‘3/4 took less than 44 minutes to queue at the North entrance', North as ¾ took less than 60 minutes at the South Entrance’, OR Indicates or unambiguously implies ‘South Entrance’ with a suitable reason, e.g. ‘25% people in 20 minutes at South entrance compared with 24 minutes at the North entrance’ | E1 | Implies that the majority of people got through quicker at the North Entrance Allow, e.g. ‘North Entrance, most people 44 minutes whilst South it was 60 minutes’ Do not accept indication of ‘South Entrance’ with a reason based on the team being slower, e.g. ‘time was taken to search of handbags’ |