Large data set fluency Worked Solutions — A-Level Maths

Fully worked, step-by-step solutions to A-Level Large data set fluency questions. See exactly how to solve problems on mean, summary statistics, median, range.

meansummary statisticsmedianrangespreadmaximum
A-Level70 questionsStep-by-step solutions
Question 1
2 markseasy
The daily mean temperature (°C) recorded at Heathrow on 8 days was: 15, 17, 16, 18, 14, 16, 15, 17. Calculate the mean daily temperature.

Worked solution

  1. Write the mean formula

    xˉ=∑xn\bar{x}=\dfrac{\sum x}{n}

    The mean equals the total of the readings divided by how many there are.

  2. Add all the readings

    ∑x=14+15+15+16+16+17+17+18=128\sum x=14+15+15+16+16+17+17+18=128

    Total the readings in the extract.

  3. Divide the total by n

    xˉ=1288=16\bar{x}=\dfrac{128}{8}=16

    The mean is the total divided by how many readings there are.

Answer
1616
Question 2
2 markseasy
The daily maximum gust (knots) on 5 days was: 12, 15, 11, 14, 13. Find the median gust.

Worked solution

  1. State what the median is

    median=central ordered value\text{median}=\text{central ordered value}

    Order the values and take the middle one.

  2. Order the data

    ordered: 11, 12, 13, 14, 15\text{ordered: }11,\ 12,\ 13,\ 14,\ 15

    Write the readings in ascending order first.

  3. Locate the middle value

    Q2=13Q_2=13

    With the data ordered, the median is the central value.

Answer
1313
Question 3
2 markseasy
The daily total rainfall (mm) on 6 days was: 0, 2, 5, 1, 8, 3. Work out the range of the rainfall.

Worked solution

  1. Recall the range formula

    range=max⁡−min⁡\text{range}=\max-\min

    The range is the largest reading minus the smallest.

  2. Order the data

    ordered: 0, 1, 2, 3, 5, 8\text{ordered: }0,\ 1,\ 2,\ 3,\ 5,\ 8

    Write the readings in ascending order first.

  3. Compute the range

    range=8−0=8\text{range}=8-0=8

    Range is largest minus smallest.

Answer
88
Question 4
2 markseasy
The daily mean windspeed (knots) over 5 days was: 9, 12, 7, 15, 10. Write down the maximum windspeed.

Worked solution

  1. Decide what is required

    identify the largest reading\text{identify the largest reading}

    We simply need the greatest value in the list.

  2. Order the data

    ordered: 7, 9, 10, 12, 15\text{ordered: }7,\ 9,\ 10,\ 12,\ 15

    Write the readings in ascending order first.

  3. Identify the largest reading

    max⁡=15\max=15

    The greatest value in the extract.

Answer
1515
Question 5
2 markseasy
The daily minimum temperature (°C) over 5 days was: 6, 9, 4, 7, 5. Write down the minimum temperature.

Worked solution

  1. Decide what is required

    identify the smallest reading\text{identify the smallest reading}

    We need the least value in the list.

  2. Order the data

    ordered: 4, 5, 6, 7, 9\text{ordered: }4,\ 5,\ 6,\ 7,\ 9

    Write the readings in ascending order first.

  3. Identify the smallest reading

    min⁡=4\min=4

    The least value in the extract.

Answer
44

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