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Numeracy Higher November 2016 Unit 1 Q8

WJECHigherCurrent spec15 marksHistogramsPercentages

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.

Histogram: Frequency density against Time (hours, 0 to 4); 0 to 1: 2, 1 to 1.5: 6, 1.5 to 2: 8, 2 to 2.5: 10, 2.5 to 3: 4, 3 to 4: 1

The competition organisers also recorded the mass of every fish caught.

This is shown in the histogram below.

Histogram: Frequency density against Mass (kg, 0 to 2.0); 0 to 0.25: 8, 0.25 to 0.5: 32, 0.5 to 0.75: 40, 0.75 to 1.0: 24, 1.0 to 1.25: 32, 1.25 to 1.5: 16, 1.5 to 2.0: 4
(a)

Last year, how many of the fish caught had a mass of less than 250 g? [1]

(b)

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]

(c)

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 ……………

(d)

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

(e)

Approximately 10% of the anglers this year caught their first fish within 1 hour.

(i)

How does this percentage compare with last year’s percentage?
You must show all your working. [3]

(ii)

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]

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