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The cumulative frequency graph shows the distribution of the heights of members of a rowing club - OCR - GCSE Maths - Question 13 - 2019 - Paper 4
Question 13
The cumulative frequency graph shows the distribution of the heights of members of a rowing club. (i) Find the median.
Worked Solution & Example Answer:The cumulative frequency graph shows the distribution of the heights of members of a rowing club - OCR - GCSE Maths - Question 13 - 2019 - Paper 4
Step 1
Find the median
Answer
To find the median, we need to determine the total number of members represented in the cumulative frequency graph.
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Determine Total Members: Observe the highest value on the cumulative frequency scale in the graph, which appears to be 120 members.
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Calculate median position: The median is the value that separates the higher half from the lower half. Thus, the position of the median is given by:
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Locate the median on the graph: Draw a horizontal line at the cumulative frequency of 60 on the graph and find where it intersects the curve. From this intersection, draw a vertical line down to the x-axis to determine the corresponding height.
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Read the height: If the intersection occurs between the height values of 160 cm and 170 cm based on the graph, this indicates that the median height is likely within this range.
Thus, the median height of the members of the rowing club is found to be approximately 166 cm, taking into account mid-range estimates and the values on the graph.