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The box plot shows the distribution of the marks scored by some boys in a test - OCR - GCSE Maths - Question 12 - 2019 - Paper 1
Question 12
The box plot shows the distribution of the marks scored by some boys in a test. (a) Find the interquartile range. (b) The marks for some girls in the same test are... show full transcript
Worked Solution & Example Answer:The box plot shows the distribution of the marks scored by some boys in a test - OCR - GCSE Maths - Question 12 - 2019 - Paper 1
Step 1
Find the interquartile range.
Answer
To find the interquartile range (IQR) from the box plot:
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Identify the lower quartile (Q1) and the upper quartile (Q3). From the box plot:
- Q1 (25th percentile) is 50
- Q3 (75th percentile) is 70
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Calculate the interquartile range using the formula:
Substituting the values:
Therefore, the interquartile range is 20.
Step 2
Draw a box plot to show the distribution of marks scored by the girls.
Answer
To draw the box plot for the girls:
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Identify Key Values:
- Lowest mark: 32
- Q1: This can be calculated as Q3 - IQR = 66 - 12 = 54
- Median (Q2): 58
- Q3: 66
- Highest mark can be calculated as Lowest + Range = 32 + 44 = 76
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Draw the Number Line:
- Draw a straight horizontal line representing marks from 30 to 80.
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Plot Box:
- Draw a box from Q1 (54) to Q3 (66).
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Mark Median:
- Draw a line inside the box at the median (58).
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Whiskers:
- Extend a line (whisker) from the box to the lowest mark (32) and the highest mark (76).
The box plot will visually represent the distribution of marks for the girls as per the provided summary.
Step 3
Is her statement correct? Explain your reasoning.
Answer
Eleanor’s statement can be examined by comparing the interquartile ranges.
- The interquartile range for the boys is 20 (as calculated above).
- The interquartile range for the girls is 12 (given).
- Since the IQR for boys (20) is greater than the IQR for girls (12), it indicates that there is more variability in the boys' scores than in the girls' scores within the middle 50% of the data.
However, stating that boys did 'better' needs clarification; a larger IQR does not imply better performance, just more variability. Therefore, Eleanor's assertion focuses on variability rather than performance, which makes her statement misleading.