Bar Charts & Pictograms: WJEC GCSE Numeracy Intermediate November 2022 Unit 2 Q3

Numeracy Intermediate November 2022 Unit 2 Q3

3. The frequency diagrams below show the lengths of time that men and women spent training in the gym on Friday.

(a) Freddie says he spent exactly 1 hour 25 minutes training in the gym on Friday.
Explain how you know that Freddie is not telling the truth. [1]

(b) How many men spent less than 20 minutes training in the gym on Friday?
Circle your answer. [1]

12 14 54 6 20

14 26 34 38 76

(d) Gwen says,

“A greater proportion of women than men spent between 40 and 60 minutes training in the gym on Friday.”

Is Gwen’s statement true or false?

True ☐ False ☐

You must show all your working to support your answer. [5]

Mark scheme (a)

Scheme	Marks	Comments
Reasonable explanation, e.g. ‘no one spent longer than 80 minutes training’ ‘1 hour 25 minutes is more than 80 minutes’	E1	Allow, e.g. ‘graph only goes up to 80 (minutes)’ ‘only shows to 1 hour 20 minutes’ ‘doesn’t show above 80 minutes’ ‘the graph doesn’t extend that much’ ‘the bar doesn’t go up to 1 hour 25 minutes’ ‘the bar doesn’t go up to 85 minutes’ ‘no one spent 1 hour 25 minutes in the gym’ ‘the maximum he could have spent was 1 hour 20 minutes’ ’85 minutes was not recorded’ ‘goes no later than 1 hour 20 minutes’ Do not accept, e.g. ‘the graph only gives 20 minute time groups (slots)’ ‘because in a frequency graph there is no way to know who is Freddie’ ‘he spent 1 hour 20 minutes in the gym’ ‘he spent an hour in the gym’ ‘the graph shows he didn’t spend 1 hour 25 minutes in the gym’ ‘1 hour 25 minutes is 85 minutes’

Scheme	Marks	Comments
14	B1

Scheme	Marks	Comments
38	B1

Mark scheme (d)

Scheme	Marks	Comments
(Total number of men) 14 + 22 + 48 + 16 OR (Total number of women) 12 + 26 + 54 + 22	M1	Check the graphs for working FT ‘their 12 + 26’ from (c), i.e. ‘their 38’ + 54 + 22
(Total men) 100 AND (Total women) 114	A2	A1 for either total correct
Method considering proportions, e.g. sight of any of: \(\dfrac{48}{100}\) AND \(\dfrac{54}{114}\) 48% of 114 \(\dfrac{54}{114}\) of 100	M1	FT ‘their 48, 100, 54, and 114’ providing at least two of them are correct and ‘their total for men 100’ ≠ ‘their total for women 114’
‘False’ unambiguously selected or implied and accurate appropriate calculations to justify choice of ‘False’, e.g. 48% and 47(.3...)% or 47.4% 0.48 and 0.47(3...) (48% of 114 =) 54.7(2) and 54 (women)	A1	Allow ‘True’ if justified by correct calculations from their 4 values.