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The cumulative frequency graph shows information about the marks scored by a group of 80 students in a test - OCR - GCSE Maths - Question 15 - 2018 - Paper 5
Question 15
The cumulative frequency graph shows information about the marks scored by a group of 80 students in a test. (a) Find the interquartile range. (b) The ratio of the... show full transcript
Worked Solution & Example Answer:The cumulative frequency graph shows information about the marks scored by a group of 80 students in a test - OCR - GCSE Maths - Question 15 - 2018 - Paper 5
Step 1
Find the interquartile range.
Answer
To find the interquartile range (IQR), we need to locate the first quartile (Q1) and the third quartile (Q3) from the cumulative frequency graph.
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Calculate Q1: The first quartile (Q1) corresponds to the 25th percentile. As there are 80 students, Q1 is at the position of 0.25 * 80 = 20. Locate the 20th position on the cumulative frequency graph and find the corresponding mark.
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Calculate Q3: The third quartile (Q3) corresponds to the 75th percentile. For 80 students, Q3 is at the position of 0.75 * 80 = 60. Locate the 60th position on the graph and find the corresponding mark.
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Calculate IQR: The interquartile range is calculated as follows: . Substitute the values of Q3 and Q1 to find the IQR.
Step 2
Find the minimum mark needed to pass the test.
Answer
Given the ratio of students passing to failing the test is 4:1, we denote:
- Let x be the number of students failing the test.
- Then the number passing the test is 4x.
- The total number of students is 80, so:
Which simplifies to:
This means 16 students failed and 64 students passed the test. To find the minimum mark needed to pass, we look for the mark corresponding to the 64th student in the cumulative frequency graph, which will indicate the threshold mark for passing.