Numeracy Higher November 2016 Unit 1 Q8
8. The Big Fish Cymru annual fishing competition is held on the west coast of Wales.
Information about last year’s competition is displayed in the Big Fish Cymru booklet.
A section of this booklet is shown below.
The competition organisers recorded the time taken for each angler to catch their first fish.
This is shown in the histogram below.

The competition organisers also recorded the mass of every fish caught.
This is shown in the histogram below.

Last year, how many of the fish caught had a mass of less than 250 g? [1]
Last year, the final angler to catch their first fish did so after \(3\tfrac{1}{2}\) hours.
How many other anglers took more than 3 hours to catch their first fish? [1]
The number of anglers taking part this year was three times as many as took part last year.
How many anglers took part in the competition this year? [4]
Number of anglers this year was ……………
The median mass of the fish caught this year was 0·9 kg.
What is the difference, in kg, between the median mass of the fish caught this year and the median mass of the fish caught last year? [5]
Difference in mass is …………… kg
Approximately 10% of the anglers this year caught their first fish within 1 hour.
How does this percentage compare with last year’s percentage?
You must show all your working. [3]
Do you think it is fair to compare last year’s competition results with this year’s competition results?
You must give a reason for your answer. [1]
| Scheme | Marks | Comments |
|---|---|---|
| 2 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| 0 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| Selects to use 1st histogram and work with area, sight of any single area calculated is sufficient | S1 | Note: check histogram for working |
| 1×2 + 0.5×6 + 0.5×8 + 0.5×10 + 0.5×4 + 1×1 (= 2 + 3 + 4 + 5 + 2 + 1) | M1 | Allow one error |
| 17 (anglers last year) | A1 | CAO |
| 51 (anglers this year) | B1 | FT 3×'their 17' provided S1 previously awarded and their final answer is an integer |
| Scheme | Marks | Comments |
|---|---|---|
| Number of fish caught last year 8×0.25 + 32×0.25 + 40×0.25 + 24×0.25 + 32×0.25 + 16×0.25 + 4×0.5 | M1 | Note: check histogram for working Allow one error (= 2 + 8 + 10 + 6 + 8 + 4 + 2) |
| 40 (fish caught last year) | A1 | CAO |
| Median is the 20th or 20.5th fish | B1 | FT ‘half their 40’ or ‘half their 40' + 0.5 |
| Last year median fish weighed 0.75 (kg) | B1 | FT ‘half their 40’ or ‘half their 40' + 0.5, provided their answer is in the range 0.5 to 1.25 inclusive |
| Difference is 0.15 (kg) | B1 | FT 0.9 – ‘their 0.75’ correctly evaluated, or reversed if their 0.75 > 0.9 provided M1 previously awarded |
| Scheme | Marks | Comments |
|---|---|---|
| (i) (Percentage last year within 1 hour) 2/17 (×100 %) or equivalent | M1 | FT from (c), ‘their 2’/’their 17’, including if not working with area |
| Appropriate statement e.g. 2/17 > 1/10, 2/17 > 2/20, 11(.76… %) or 12% > 10%, or equivalent | A2 | OR as two A1s: A1 for 11(.76… %) or 12% A1 for an appropriate conclusion from ‘their 11(.76… %) or 12%’ e.g. ‘this is greater than 10%’, ‘not quite as good as last year’, ‘quite similar to last year’, ‘proportionally about the same’ OR A1 only for 2/17 > 10% Alternative 10% of 17 = 1.7 M1 1.7 < 2 A2 |
| (ii) Reflection, e.g. ‘no, as the number taking part is nowhere near the same’. ‘no, as the competition has grown’, ‘no, as the conditions might not have been the same’, ‘no, as the weather conditions could have been very different’ | E1 | 'No' may be stated or implied Accept 'Yes' provided their reason has reference to comparing like with like e.g. proportions, percentages |