Show — 3 marks
A local shop records the number of customers and the total sales, in pounds, for six days. The table shows the results.
| Number of customers | 15 | 25 | 35 | 45 | 55 | 65 |
|---------------------|----|----|----|----|----|----|
| Sales (£) | 120| 200| 280| 360| 440| 520|
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(a) On the grid, show the point that represents 35 customers and £280 sales.
[1 mark]
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(b) Show that there is positive correlation between the number of customers and the sales.
[2 marks]
Show mark scheme
- (a) Point plotted correctly at (35, 280)
- (b) States that as number of customers increases, sales also increase
- (b) Reference to values from the table or pattern shown in plotted points
State — 5 marks
A retail company collects data on 12 stores to investigate the relationship between the number of staff employed and the weekly sales revenue. The data collected is shown in the table below.
Number of staff: 8, 12, 15, 10, 18, 6, 14, 9, 16, 11, 13, 7
Weekly sales (£000s): 24, 38, 45, 32, 52, 18, 42, 28, 48, 35, 40, 22
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(a) State the type of correlation shown between the number of staff and weekly sales revenue.
[1 mark]
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(b) State whether it would be correct to conclude that employing more staff causes an increase in weekly sales revenue. Give a reason for your answer.
[2 marks]
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(c) Two points from the data are \((8, 24)\) and \((18, 52)\). A line of best fit is drawn through these two points. State the gradient of this line, giving your answer as a simplified fraction.
[2 marks]
Show mark scheme
- (a) Correctly states positive correlation (or strong positive correlation)
- (b) States no (or it would not be correct)
- (b) Provides valid reason such as: correlation does not prove causation / there may be other factors affecting sales / the relationship could be coincidental
- (c) Correctly calculates gradient as \(\frac{52 - 24}{18 - 8} = \frac{28}{10}\)
- (c) Simplifies to \(\frac{14}{5}\) (or \(2.8\) accepted as equivalent decimal form)
State — 5 marks
A financial analyst investigates the relationship between house prices and the number of years since a property was last renovated. Data from 10 properties in a town shows the following values:
Years since renovation: 2, 5, 3, 8, 1, 6, 4, 9, 7, 2
House price (£1000s): 285, 210, 265, 155, 310, 190, 240, 120, 170, 295
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(a) State the type of correlation between the number of years since renovation and house price.
[2 marks]
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(b) State whether it would be correct to conclude that renovating a house will cause its price to increase. Give a reason for your answer.
[3 marks]
Show mark scheme
- (a) Identifies negative correlation (or strong negative correlation)
- (a) Correctly identifies that as years since renovation increases, house price decreases
- (b) States 'No' or 'It would not be correct'
- (b) Identifies that correlation does not prove causation
- (b) Recognises that other factors (location, size, condition, market changes) could affect price, not just renovation age
Compare — 3 marks
A financial analyst collects data on 10 small businesses. For each business, they record the amount spent on staff training (in £1000s) and the annual profit (in £10000s). The data collected is: Training spend: 2, 3, 3, 4, 5, 6, 6, 7, 8, 9. Profit: 5, 7, 6, 9, 11, 12, 11, 14, 15, 17.
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(a) Describe the correlation between staff training spend and annual profit shown by this data.
[1 mark]
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(b) Compare the following two statements and explain which one is correct:
Statement A: "Because there is a strong positive correlation between training spend and profit, spending more on training will always cause a business to make more profit."
Statement B: "There is a strong positive correlation between training spend and profit, but this does not prove that training causes higher profit."
[2 marks]
Show mark scheme
- (a) Identifies strong positive correlation (or equivalent description such as 'as training spend increases, profit increases' or 'positive relationship')
- (b) Correctly identifies Statement B as correct
- (b) Explains that correlation does not prove causation, or acknowledges that other factors might affect profit (such as market conditions, management quality, or business type), or notes that Statement A incorrectly assumes cause from correlation
Show — 4 marks
A property manager records data about residential flats in a city. For 10 flats, they note the distance from the city centre (in kilometres) and the monthly rental price (in pounds). The data collected is shown in the table below.
Distance from city centre (km): 0.5, 1.2, 1.8, 2.3, 2.9, 3.5, 4.1, 4.8, 5.2, 6.0
Monthly rental price (£): 1200, 1150, 1050, 950, 900, 850, 750, 700, 650, 600
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(a) Describe the type of correlation between the distance from the city centre and the monthly rental price. Explain what this correlation tells you about the relationship between these two variables.
[2 marks]
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(b) Show that it would be incorrect to conclude that living further from the city centre causes rental prices to decrease. Give one alternative explanation for the correlation observed.
[2 marks]
Show mark scheme
- (a) Identifies the correlation as negative (or strong negative)
- (a) Explains that as distance increases, rental price decreases (or equivalent statement about the relationship)
- (b) Correctly states that correlation does not prove causation (or that other factors could be involved)
- (b) Provides a plausible alternative explanation, such as: quality of the flat, age of the building, local amenities, transport links, neighbourhood characteristics, or other relevant factor
GCSE Perfect