Higher June 2022 Paper 2 Q14

14 A survey was held in a football stadium.

A sample of the crowd was asked about the importance of a family area.

The pie chart represents the answers.

(a) The total number of people in the crowd was 29 250

Estimate how many people in the crowd think that a family area is very important.

Assume that the sample is representative of the crowd. [3 marks]

(b) In fact,

What is this likely to mean about the actual number of people in the crowd who think that a family area is very important?

Tick one box. [1 mark]

Mark scheme (a)

Answer	Mark	Comments
Alternative method 1
\(375 + 400 + 1475\) or 2250 or 13 seen or \(\dfrac{59}{90}\) seen or [0.65, 0.66] seen	M1	oe for 375 allow 350 or 370 or 380 or 400 for 1475 allow 1450 or 1470 or 1480 or 1500 eg \(400 + 400 + 1500\) any estimated values must be seen eg only seeing 2300 is M0
\(\dfrac{1475}{375 + 400 + 1475} \times 29\,250\) or \(1475 \times 13\) or [0.65, 0.66] \(\times\) 29 250 or [19012.5, 19305]	M1dep	oe for 375 allow 350 or 370 or 380 or 400 for 1475 allow 1450 or 1470 or 1480 or 1500 for 29 250 allow 29 000 or 29 200 or 29 300 or 29 500 or 30 000
19 175	A1
Alternative method 2
[234, 238]	M1	may be on the diagram
\(\dfrac{\text{their } [234, 238]}{360} \times 29\,250\) or their [234, 238] \(\times\) 81.25	M1dep	oe for 29 250 allow 29 000 or 29 200 or 29 300 or 29 500 or 30 000
19 175	A1

\(375 + 400 + 1475 = 2250\) If they subsequently estimate 2250 no further marks can be scored	M1
Answer 19 175 is M1M1A1 unless it comes from rounding or truncating
eg1 Alt 1 \(0.65555 \times 29\,250 = 19\,175\)	M1M1A1
eg2 Alt 1 \(0.65555 \times 29\,250 = 19\,174.8\) Answer 19 175	M1M1A0
Alt 2 if their angle is outside the range [234, 238]	M0M0A0