The table gives information about the times taken, in seconds, by 18 students to run a race. | Time (s) | Frequency | | ------------ | --------- | | 5 < t ≤ 10 | 1 | | 10 < t ≤ 15 | 2 | | 15 < t ≤ 20 | 7 | | 20 < t ≤ 25 | 8 | Work out an estimate for the mean time. Give your answer correct to 3 significant figures.

GCSE Edexcel Maths Standard & Compound Units: The table gives information abou

The table gives information about the times taken, in seconds, by 18 students to run a race - Edexcel - GCSE Maths - Question 5 - 2019 - Paper 3

Question 5

The table gives information about the times taken, in seconds, by 18 students to run a race. | Time (s) | Frequency | | ------------ | --------- | | 5 < t ≤ 10 ... 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 5 - 2019 - Paper 3

Step 1

Step 1: Calculate Midpoints

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Answer

To estimate the mean time, first, we need to calculate the midpoints for each time interval:

For the interval $5 < t \leq 10$ : midpoint = ( \frac{5 + 10}{2} = 7.5 )
For the interval $10 < t \leq 15$ : midpoint = ( \frac{10 + 15}{2} = 12.5 )
For the interval $15 < t \leq 20$ : midpoint = ( \frac{15 + 20}{2} = 17.5 )
For the interval $20 < t \leq 25$ : midpoint = ( \frac{20 + 25}{2} = 22.5 )

Step 2

Step 2: Multiply Midpoints by Frequencies

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Answer

Next, we multiply each midpoint by its corresponding frequency:

$7.5 \times 1 = 7.5$
$12.5 \times 2 = 25$
$17.5 \times 7 = 122.5$
$22.5 \times 8 = 180$

Step 3

Step 3: Sum of Products and Frequencies

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Now, we sum these products:

[ 7.5 + 25 + 122.5 + 180 = 335 ]

And also sum the frequencies:

[ 1 + 2 + 7 + 8 = 18 ]

Step 4

Step 4: Calculate the Mean

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Answer

The estimated mean time is given by the formula:

[ \text{Mean} = \frac{\text{Total of products}}{\text{Total frequency}} = \frac{335}{18} \approx 18.61 ]

Rounding this to 3 significant figures gives us:

Mean time = 18.6 seconds

The table gives information about the times taken, in seconds, by 18 students to run a race - Edexcel - GCSE Maths - Question 5 - 2019 - Paper 3

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 5 - 2019 - Paper 3

Step 1: Calculate Midpoints

Step 2: Multiply Midpoints by Frequencies

Step 3: Sum of Products and Frequencies

Step 4: Calculate the Mean

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