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The box plot shows the distribution of the salaries for the workers at Bexbridge Biscuits - OCR - GCSE Maths - Question 16 - 2018 - Paper 1

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The box plot shows the distribution of the salaries for the workers at Bexbridge Biscuits. (a) State the median salary. (b) Find the interquartile range. (c) The ... show full transcript

Worked Solution & Example Answer:The box plot shows the distribution of the salaries for the workers at Bexbridge Biscuits - OCR - GCSE Maths - Question 16 - 2018 - Paper 1

Step 1

State the median salary.

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Answer

The median salary of the workers at Bexbridge Biscuits is £37,000. This can be observed directly from the box plot, where the line inside the box indicates the median.

Step 2

Find the interquartile range.

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Answer

The interquartile range (IQR) is calculated as the difference between the upper quartile and the lower quartile. From the box plot:

  • Lower Quartile (Q1) = £28,000
  • Upper Quartile (Q3) = £50,000

Thus, the IQR is calculated as follows:

IQR=Q3Q1=50,00028,000=£22,000IQR = Q3 - Q1 = 50,000 - 28,000 = £22,000

Step 3

Draw a box plot to show the salaries of the workers at Camford Cookies.

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Answer

To draw the box plot for Camford Cookies, note the following values:

  • Lower Quartile (Q1) = £28,000
  • Median = £37,000
  • Upper Quartile (Q3) = £50,000
  • Maximum = £85,000
  • Minimum = £17,000 (which is 20% of the highest salary, £85,000)

The box plot will reflect these values accordingly.

Step 4

Make two different comparisons between the distribution of the salaries at Bexbridge Biscuits and the salaries at Camford Cookies.

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Answer

  1. The median salary at Bexbridge Biscuits (£37,000) is the same as the median salary at Camford Cookies.

  2. The interquartile range for Bexbridge Biscuits (£22,000) is the same as that for Camford Cookies, indicating that the spread of the middle 50% of salaries is similar in both distributions.

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