Higher June 2017 Paper 2 Q14
14. A store manager measured the length of the electrical cords on 60 different hairdryers.
The cumulative frequency diagram illustrates the store manager’s findings.
(a) How many electrical cords are between 1·6 m and 2 m in length? [1]
(b) The store had a target:
Give a reason for your answer.
State any assumption you made when calculating your answer.
You must show all your working. [3]
- at least 75% of hairdryers checked should have an electrical cord longer than 100 cm.
Give a reason for your answer.
State any assumption you made when calculating your answer.
You must show all your working. [3]
(c)
(i) Use the cumulative frequency diagram to estimate the median length of the electrical cords. [1]
(ii) The store manager realised that she had measured the shortest electrical cord incorrectly.
The cord actually measures 79 cm.
What impact does this have on the median?
You must give a reason for your answer. [1]
The cord actually measures 79 cm.
What impact does this have on the median?
You must give a reason for your answer. [1]
| Scheme | Marks | Comments |
|---|---|---|
| 8 (cords) | B1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
Interpretation and ‘Yes’, stated or implied, with a suitable correct calculation, e.g. ‘yes’ with
| B2 | B1 for 0.75 × 60, or 0.25 × 60, or 15/60, or 45/60, or 12/60, or 48/60, or sight of reading at LQ 108 (cm) (accept 106 cm to 110 cm) |
| Assumption, e.g. ‘assumed all the lengths were evenly distributed’ | E1 | Depends on B1. Stated or implied Allow, e.g. ‘the reading for the group(s) at upper bound’ Accept, e.g. ‘Target not met, as the relationship is probably not linear’ Do not accept, e.g. ‘my readings from the diagram were not accurate’, ‘measurements were inaccurate’ |
| Scheme | Marks | Comments |
|---|---|---|
| (i) Answers in the range 132 to 136 (cm) inclusive | B1 | |
| (ii) No impact and gives a reason, e.g. states median is as (c)(i) and states, e.g. ‘still less than 80 cm’, or ‘still below the median’ | E1 | |
| (6) |