Study Hours Analysis using Cumulative Frequency Graph
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7 marks
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A group of 150 students were asked how many hours they spent studying mathematics in a particular week. Interpret the provided cumulative frequency graph below, which details the relationship between hours studied (ranging from 0 to 10) and the cumulative count of students (ranging from 0 to 150).nnnn(a) Find the median number of hours studied. [2]n(b) Find the number of students who studied for more than 6 hours. [2]n(c) Calculate the interquartile range. [3]
Part a
2 minutes
2 marks
Question
Find the median number of hours studied. [2]
Hint Hint
Hint
Locate the 75th student on the cumulative frequency curve (half of 150) and read the corresponding x-value.
Answer Answer
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Complete Answer
Median ≈ 4.8 hours
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Part b
2 minutes
2 marks
Question
Find the number of students who studied for more than 6 hours. [2]
Hint Hint
Hint
Read the cumulative frequency at 6 hours from the graph and subtract that value from the total number of students.
Answer Answer
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Explanation Explanation
Answer Answer
Complete Answer
40 students
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Part c
4 minutes
3 marks
Question
Calculate the interquartile range. [3]
Hint Hint
Hint
Find Q1 (at the 37.5th student) and Q3 (at the 112.5th student) from the graph, then subtract Q1 from Q3.
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