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Year 8

Calculating the mean

I can calculate the mean from data presented in a frequency table and different graphs.

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New
New
Year 8

Calculating the mean

I can calculate the mean from data presented in a frequency table and different graphs.

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Share activities with pupils
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Lesson details

Key learning points

  1. The mean can be calculated from a line graph.
  2. The mean can be calculated from an ungrouped frequency table.
  3. The mean can be calculated from a bar chart.

Keywords

  • Frequency - The frequency is the number of times an event occurs; or the number of individuals (people, animals etc.) with some specific property.

  • Data - Data are a collection of information.

  • Mean - The sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.

  • Measure of central tendency - A summary measure that attempts to describe a whole set of data with a single value that represents the middle of the distribution.

Common misconception

Pupils may divide by how many groups/bars there are, instead of the total frequency.

By reminding students frequently that averages need to give a 'typical' value of the data set, ask them to sense check their mean value.

Pupils should be encouraged to articulate what each part of the table or chart is representing in the context of the data.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of these frequency tables shows 49 pieces of data?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q2.
The bar chart shows the number of children who have visited different attractions in the summer holidays. The bar for has a frequency of 12.
An image in a quiz
Correct Answer: Zoo, zoo
Q3.
Laura times her bus journey to school every day for a week. On which day did Laura's journey take 28 minutes?
An image in a quiz
Monday
Tuesday
Wednesday
Correct answer: Thursday
Friday
Q4.
A measure of central tendency is a summary measure that attempts to describe a whole set of with a single value that represents the middle or centre of its distribution.
Correct Answer: data
Q5.
A large data set has 452 data values which have a total of 16 724. The mean of the data is .
Correct Answer: 37, thirty seven, thirty-seven
Q6.
The mean for the data shown on this dot plot is .
An image in a quiz
Correct Answer: 6, six

Exit quiz

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6 Questions

Q1.
Select all the data sets that have a mean.
Correct answer: 4, 5, 8, 0, 2, 5
Correct answer: 3.1, 4.4, 7.3, 8.0, 9.4
tea, coffee, tea, tea, coffee, tea, water
Correct answer: -6, -4, -3, -8, 4, 7, 8
rose, tulip, daffodil
Q2.
The (arithmetic) mean for a set of data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.
Correct Answer: numerical, qualitative
Q3.
Without any further calculation, which of these could be the mean?
An image in a quiz
Correct answer: 2.53
10
16
58
147
Q4.
Laura records how long her journey is to school each day for a week. The line graph shows her results. Laura's mean journey time is minutes.
An image in a quiz
Correct Answer: 28.2
Q5.
The bar chart shows the number of goals scored by a club in a season. 192 goals were scored in total. The mean number of goals per match is rounded to 1 decimal place.
An image in a quiz
Correct Answer: 2.2
Q6.
Which of these calculations is correct for finding the mean from this frequency table?
An image in a quiz
$$ {6+7+6+12+14}\over{5}$$
$$ {6+7+6+12+14}\over{10}$$
$$ {0+7+12+36+56}\over{5}$$
$$ {6+7+12+36+56}\over{6+7+6+12+14}$$
Correct answer: $$ {0\times6+1\times7+2\times6+3\times12+4\times14}\over{6+7+6+12+14}$$