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The table shows information about the heights, in cm, of a group of Year 11 girls - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 1
Question 12
The table shows information about the heights, in cm, of a group of Year 11 girls. | height (cm) | |------------------| | least height | 154 | | median ... show full transcript
Worked Solution & Example Answer:The table shows information about the heights, in cm, of a group of Year 11 girls - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 1
Step 1
Draw a box plot for this information.
Answer
To create the box plot for Year 11 girls, we need to identify the key values from the data provided:
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Least Height: 154 cm
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Lower Quartile (Q1): 161 cm
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Median (Q2): 165 cm
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Upper Quartile (Q3): Since the interquartile range (IQR) is 7, we can calculate the upper quartile as follows:
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Highest Value: To find the highest value, we can use the range information:
Thus, we can now plot the box plot:
- The lower whisker extends from 154 to 161.
- The box covers from 161 to 168, with a line at 165 for the median.
- The upper whisker extends from 168 to 174.
Step 2
Compare the distribution of heights of the Year 7 girls with the distribution of heights of the Year 11 girls.
Answer
In comparing the distributions:
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Median: The median height of Year 11 girls is 165 cm. If it is higher than the Year 7 median (not provided in the question), it suggests that Year 11 girls are generally taller.
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Interquartile Range (IQR): For Year 11, the IQR is 7 cm. If Year 7 has a lower IQR, it indicates that their heights are less spread out than those of Year 11 girls.
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Range: The range for Year 11 is 20 cm. If Year 7 has a narrower range, it further indicates that Year 7 girls display less variability in heights.
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Spread and Distribution: A smaller IQR and range, combined with a lower median, would suggest that Year 7 girls have more uniform heights compared to Year 11 girls who show greater variation in height. Additionally, any skewness in the box plots (left or right) could indicate how the distributions differ further.