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The table gives some information about the heights of 80 girls - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 1
Question 10
The table gives some information about the heights of 80 girls. Least height: 133 cm Greatest height: 170 cm Lower quartile: 145 cm Upper quartile: 157 cm Median: 1... show full transcript
Worked Solution & Example Answer:The table gives some information about the heights of 80 girls - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 1
Step 1
Draw a box plot to represent this information
Answer
To draw a box plot, we need to identify the five key values: the least height, lower quartile, median, upper quartile, and greatest height.
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Plot the Minimum Value (Least Height): Mark the lowest value at 133 cm on the horizontal axis.
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Plot the Lower Quartile: Mark the lower quartile at 145 cm.
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Plot the Median: Mark the median at 151 cm.
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Plot the Upper Quartile: Mark the upper quartile at 157 cm.
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Plot the Maximum Value (Greatest Height): Mark the highest value at 170 cm.
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Draw the Box: Create a box from the lower quartile (145 cm) to the upper quartile (157 cm).
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Draw the Whiskers: Extend lines (whiskers) from the ends of the box to the minimum height (133 cm) and maximum height (170 cm).
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Label the Box Plot: Ensure to label the height (cm) on the x-axis and display the entire range clearly.
Step 2
Work out an estimate for the number of these girls with a height between 133 cm and 157 cm
Answer
To estimate the number of girls with a height between 133 cm and 157 cm:
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Identify the Range: The heights in this range are from the least height (133 cm) to the upper quartile (157 cm).
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Determine the Total Number of Girls: The total number of girls is 80.
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Estimate the Proportion of Girls within the Range: The lower quartile (145 cm) divides the lower half of the data, while the upper quartile (157 cm) gives insight into the upper half.
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Calculate: Estimating the distribution, a rough estimate would find that girls within 133 cm to 145 cm represent about 25% of the total, and those between 145 cm and 157 cm another 25%. Therefore:
Total girls between 133 cm and 157 cm: 80 x 0.5 = 40 girls.
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Conclusion: Hence, around 40 girls are estimated to have heights in this range.