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Some people took part in the first round of a competition - Edexcel - GCSE Maths - Question 17 - 2021 - Paper 2
Question 17
Some people took part in the first round of a competition. The histogram gives information about the scores of these people in the first round. 20% of the people go... show full transcript
Worked Solution & Example Answer:Some people took part in the first round of a competition - Edexcel - GCSE Maths - Question 17 - 2021 - Paper 2
Step 1
Find the total area under the histogram
Answer
To begin, the total area under the histogram represents the total number of participants. The area for each bar can be calculated by multiplying the width by the height:
- For the first bar (0-10): Area = 10 x 2 = 20
- For the second bar (10-20): Area = 10 x 3 = 30
- For the third bar (20-30): Area = 10 x 2 = 20
- For the fourth bar (30-40): Area = 10 x 1 = 10
Now, sum these areas:
Total Area = 20 + 30 + 20 + 10 = 80 This means a total of 80 people participated.
Step 2
Step 3
Identify the qualifying score from the histogram
Answer
Next, we look at the histogram to find the score corresponding to the top 16 people. The cumulative number of people scoring from the highest score downward:
- From 30 to 40 (last bar): 10 people
- From 20 to 30 (third bar): 20 people (cumulative total: 10 + 20 = 30)
- From 10 to 20 (second bar): 30 people (cumulative total: 30 + 30 = 60)
- From 0 to 10 (first bar): 20 people (cumulative total: 60 + 20 = 80)
To find the cutoff score for the top 16 qualifiers, we see that the last 10 people scored between 30 and 40, which indicates that the lowest qualifying score is 30.