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GCSE Maths · Higher · Chapter 3: Statistical diagrams and averages · Lesson 2

Averages and spread from tables

Grades 4–7About 50 minutesCalculator allowed36 marks
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NameClassDate
A

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

  1. A1
    Needed today

    Find the median of .

    [1 mark]
    Answer
  2. A2
    Last lesson

    36 people were asked. 4 said yes. Find the angle for "yes" on a pie chart.

    [1 mark]
    Answer
  3. A3
    From chapter 1

    Work out .

    [1 mark]
    Answer
  4. A4
    Key Stage 3

    A bag holds 5 red and 3 blue counters. Find P(red).

    [1 mark]
    Answer
B

Example, then your turn

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

The table shows the times, minutes, that 30 people waited at a clinic. Work out an estimate of the mean time.

Time, t (min)Frequency0 < t ≤ 10510 < t ≤ 20820 < t ≤ 301130 < t ≤ 406
Hint Use the midpoint of each group as the value for everyone in it.
  1. B1

    The table shows the lengths, cm, of 40 fish. Work out an estimate of the mean length.

    [3 marks]
    Length, l (cm)Frequency10 < l ≤ 20820 < l ≤ 301130 < l ≤ 401340 < l ≤ 508
    Answer
C

Practice

Grades 5–6
  1. C1

    Six swimmers took 31, 32, 32, 34, 35 and 58 seconds. Which average, the mean or the median, best describes a typical time? Give a reason.

    [2 marks]
  2. C2

    12 students have a mean mark of 64. Another 8 students have a mean mark of 74. Work out the mean mark of all 20 students.

    [2 marks]
    Answer
  1. C3

    A team scored 0 goals in 4 matches, 1 in 7, 2 in 6 and 3 in 3. Work out the mean goals per match.

    [2 marks]
    Answer
  2. C4

    Five numbers have a mean of 12. One number is removed and the other four have a mean of 10.5. Which number was removed?

    [2 marks]
    Answer
  3. C5

    The table shows the number of people in each car that passed a school. The mean number of people in a car is . Work out the value of .

    [3 marks]
    People in the carFrequency162x3842
    Answer
  4. C6

    The table shows the masses, kg, of 35 dogs at a rescue centre. Which class contains the median mass?

    [2 marks]
    Mass, m (kg)Frequency0 < m ≤ 10510 < m ≤ 20920 < m ≤ 301230 < m ≤ 40640 < m ≤ 503
    Answer
D

Exam-style questions

Grades 6–7
  1. D1

    A table shows the value 1 fourteen times, 2 eleven times, 3 six times, 4 five times and 5 four times. Priya says, "The median is 3, because 3 is in the middle of 1 to 5."

    Explain why Priya is wrong, and find the median.

    [2 marks]
  1. D2

    The table shows the times, minutes, that 50 runners from club A took to run 5 km.

    Time, t (min)Frequency15 < t ≤ 20620 < t ≤ 251425 < t ≤ 301830 < t ≤ 3512
    (a)

    Write down the modal class.

    [1 mark]
    Answer
    (b)

    Work out an estimate of the mean time.

    [3 marks]
    Answer
    (c)

    The 40 runners from club B have an estimated mean time of 27.4 minutes. Work out an estimate of the mean time of all 90 runners, to 1 decimal place.

    [2 marks]
    Answer
    (d)

    Explain why your answer to (b) is an estimate.

    [1 mark]
    Total for D2: 7 marks
  2. D3

    Two shops deliver parcels. The delivery times, in days, of five parcels from each shop are: Shop P: and Shop Q: . Compare the delivery times of the two shops. Use the median and the range.

    [4 marks]
E

Extension

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    Five whole numbers have a mean of 7, a median of 7 and a range of 6. The only mode is 7. Find the five numbers.

    [3 marks]
    Hint 1 · What to try

    Write them in order as , , , , . What must they add up to?

    Hint 2 · The first line

    They add up to 35, and . The number 7 must appear more often than any other.

    Hint 3 · The full method

    With 7 three times: , so and the numbers are 4, 7, 7, 7, 10. With 7 only twice there is no answer.

    Answer
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can find the mode, median and mean from a frequency table.
I can estimate the mean from grouped data.
I can compare two sets of data and choose the average that fits them best.

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