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Numeracy Higher November 2023 Unit 2 Q2

WJECHigherCurrent spec8 marksFrequency PolygonsGrouped Data

2. Glanafon and Pencwm dog rescue centres take in unwanted dogs.

The mass of each dog in the two dog rescue centres was recorded.

Groups of width 10 kg were used:

5 kg \(\leqslant\) mass \(<\) 15 kg,   15 kg \(\leqslant\) mass \(<\) 25 kg,   …,   55 kg \(\leqslant\) mass \(<\) 65 kg

The results are shown in the frequency polygons below.

Frequency polygons of mass (kg) for Glanafon and Pencwm dog rescue centres, frequency 0 to 50, mass 0 to 70 kg
(a)

Doreen, Rory and Muzhir look at these frequency polygons.

(i)

Doreen says,

“The modal group of the masses of dogs in each dog rescue centre is the same.”

Is Doreen correct?

Yes ☐    No ☐    Can’t tell ☐

You must give a reason for your answer. [1]

(ii)

Rory says,

“28 of the dogs in Pencwm each have a mass of 18 kg.”

Is Rory correct?

Yes ☐    No ☐    Can’t tell ☐

You must give a reason for your answer. [1]

(iii)

Muzhir says,

“There is a higher proportion of dogs that are heavier than 35 kg in Glanafon than in Pencwm.”

Without doing any calculations, decide if Muzhir is correct.

Correct ☐    Incorrect ☐    Can’t tell ☐

You must give a reason for your answer. [1]

(b)

The estimate of the mean mass of the dogs in Glanafon was 32·5 kg.
How much less was the estimate of the mean mass of the dogs in Pencwm?
You must show all your working. [5]

Estimate of the mean mass of the dogs in Pencwm is …………… kg less than in Glanafon.

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