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The table shows information about the weekly earnings of 20 people who work in a shop - Edexcel - GCSE Maths - Question 5 - 2017 - Paper 1
Question 5
The table shows information about the weekly earnings of 20 people who work in a shop. Weekly earnings (£x) Frequency 150 < x ≤ 250 1 250 < x... show full transcript
Worked Solution & Example Answer:The table shows information about the weekly earnings of 20 people who work in a shop - Edexcel - GCSE Maths - Question 5 - 2017 - Paper 1
Step 1
Estimate for the mean of the weekly earnings
Answer
To estimate the mean of the weekly earnings, we can use the midpoints of each interval, multiplied by their respective frequencies, and then divide by the total number of people.
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Calculate midpoints:
- For £(150 < x ≤ 250): midpoint = 200
- For £(250 < x ≤ 350): midpoint = 300
- For £(350 < x ≤ 450): midpoint = 400
- For £(450 < x ≤ 550): midpoint = 500
- For £(550 < x ≤ 650): midpoint = 600
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Multiply midpoint by frequency:
- £200 × 1 = £200
- £300 × 11 = £3300
- £400 × 5 = £2000
- £500 × 0 = £0
- £600 × 3 = £1800
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Sum these products:
Total = £200 + £3300 + £2000 + £0 + £1800 = £5300
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Divide by total frequency (20):
Mean = £5300 / 20 = £265
Therefore, the estimated mean of the weekly earnings is £265.
Step 2
Do you agree with Nadiya?
Answer
I agree with Nadiya that the mean may not be the best average to represent this information. This is primarily because the distribution of weekly earnings is skewed, with a large number of workers earning below £350, and a few earning significantly more. The mean can be heavily influenced by extreme values (outliers), which may not accurately reflect the earnings of the majority. In such cases, it may be more appropriate to use the median, as it represents the middle value of the dataset and is less affected by outliers.