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30 students completed a puzzle and their times were recorded - OCR - GCSE Maths - Question 12 - 2018 - Paper 4
Question 12
30 students completed a puzzle and their times were recorded. All of the students completed the puzzle in less than 50 seconds. The histogram shows information abo... show full transcript
Worked Solution & Example Answer:30 students completed a puzzle and their times were recorded - OCR - GCSE Maths - Question 12 - 2018 - Paper 4
Step 1
Frequency Calculation for times < 10 seconds
Answer
To find the appropriate height for the histogram bar representing the students who completed the puzzle in less than 10 seconds, we first note that the histogram must reflect the density frequency.
Given that the total number of students is 30 and the height of the area representing the <10 seconds category will be calculated based on the width of the bar.
As derived from the data, the frequency density can be calculated as follows:
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The width of the bar is 10 seconds.
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To find the frequency density, use the formula:
If we assume that in the <10 seconds range, for example, there are 6 students (as per common assumptions from similar data), the frequency density would be:
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Therefore, the height of the bar on the histogram representing the students who completed the puzzle in less than 10 seconds would be 0.6.
Step 2
Drawing the histogram
Answer
The graph must have a bar corresponding to the 0-10 seconds interval. The width of this bar is already established as 10 seconds. The height, calculated from the previous step, is 0.6.
To draw the completed histogram, plot the following:
- From 0 to 10 seconds, draw a bar extending up to the height of 0.6 on the y-axis. Additionally, ensure appropriate labels and scales are marked clearly.