Higher November 2023 Paper 1 Q6

6 A music company releases 10 albums.

The scatter graph shows, for each album,

the number of downloads on the first day
and
the number of CDs sold on the first day.

A line of best fit has been drawn on the scatter graph.

(a) The scatter graph shows positive correlation.

Describe the relationship between number of downloads and number of CDs sold. [1 mark]

(b) The company earns

£2.50 for each download
and
£3 for each CD sold.

The company releases another album.

On the first day it has 9000 downloads.

Estimate the total amount the company earns from downloads and CDs of the album that day. [3 marks]

Mark scheme (a)

Answer	Mark	Comments
Valid description	B1	eg as downloads increase, so do CD sales downloads are about \(\left[1\dfrac{1}{3}, 2\right]\) times as many as CDs CDs are about \(\left[\dfrac{1}{2}, \dfrac{3}{4}\right]\) as many as downloads

Ignore ‘Positive correlation’
Condone references to causality eg an increase in downloads causes an increase in CDs sold	B1
As one goes up the other goes up / Both go up at a similar rate	B1
They both go up	B0
Downloads are always more than CDs	B0
They are in direct proportion	B0
The relationship is linear	B0

Mark scheme (b)

Answer	Mark	Comments
Alternative method 1 – reading from the graph
\(2.5(0) \times 9000\) or 22 500 or [5300, 5500]	M1	oe 2.5(0) may be 2 or 3 [5300, 5500] may be 5000
\(2.5(0) \times 9000 + 3 \times [5300, 5500]\) or \(22\,500 + [15\,900, 16\,500]\)	M1dep	oe 2.5(0) may be 2 or 3 [5300, 5500] may be 5000
[38 400, 39 000]	A1ft	ft 2 or 3 for 2.5(0) and/or 5000 for [5300, 5500]
Alternative method 2 – using a multiplier
\(2.5(0) \times 9000\) or 22 500 or \(9000 \times [0.5, 0.75]\)	M1	oe 2.5(0) may be 2 or 3
\(2.5(0) \times 9000 + 3 \times 9000 \times [0.5, 0.75]\)	M1dep	oe 2.5(0) may be 2 or 3
[36 000, 42 750] with \(9000 \times [0.5, 0.75]\) seen	A1ft	ft 2 or 3 for 2.5(0)

Check graph for working

Working may be in pence, units not required for up to M2
Final answer in pence must have units to award A1