The table gives information about the times taken, in seconds, by 18 students to run a race - Edexcel - GCSE Maths - Question 6 - 2019 - Paper 3
Question 6
The table gives information about the times taken, in seconds, by 18 students to run a race.
| Time (< seconds) | Frequency |
| ---------------- | --------- |
| 5 <... show full transcript
Worked Solution & Example Answer:The table gives information about the times taken, in seconds, by 18 students to run a race - Edexcel - GCSE Maths - Question 6 - 2019 - Paper 3
Step 1
Calculate midpoint for each time interval
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Answer
To estimate the mean time, we start by calculating the midpoints for each time interval:
For the interval 5 < i < 10, the midpoint is ( M_1 = \frac{5 + 10}{2} = 7.5 )
For the interval 10 < i < 15, the midpoint is ( M_2 = \frac{10 + 15}{2} = 12.5 )
For the interval 15 < i < 20, the midpoint is ( M_3 = \frac{15 + 20}{2} = 17.5 )
For the interval 20 < i < 25, the midpoint is ( M_4 = \frac{20 + 25}{2} = 22.5 )
Step 2
Multiply midpoints by their frequencies
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Answer
Next, we multiply each midpoint by its respective frequency:
For 5 < i < 10: ( 7.5 \times 1 = 7.5 )
For 10 < i < 15: ( 12.5 \times 2 = 25.0 )
For 15 < i < 20: ( 17.5 \times 7 = 122.5 )
For 20 < i < 25: ( 22.5 \times 8 = 180.0 )
Step 3
Sum the products
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Now we sum the products obtained from the previous step:
( 7.5 + 25.0 + 122.5 + 180.0 = 335.0 )
Step 4
Calculate total frequency
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Next, we calculate the total frequency:
( 1 + 2 + 7 + 8 = 18 )
Step 5
Estimate the mean time
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Finally, we estimate the mean time by dividing the total sum of the products by the total frequency:
