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Year 6

Explain how the mean changes when the total quantity or number of values changes

I can explain how the mean changes when the total quantity or number of values changes

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New

Year 6

Explain how the mean changes when the total quantity or number of values changes

I can explain how the mean changes when the total quantity or number of values changes

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Share activities with pupils

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Lesson details

Key learning points

When the total value of the set increases, the mean average increases.
When the total value of the set decreases, the mean average decreases.
When the number of values changes, the total quantity must be divided by the new number of values.

Keywords

Mean average - The mean average is a single number expressing the typical value in a set of data. It is calculated by finding the total of the set of data and dividing by how many values there are.
Set of data - A set of data is a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

Common misconception

Not realising that if you change the number of values in the set, you must divide the total by the new number of values and that this affects the value of the mean average.

Use the definition of the mean average to check that the total of the set of data is correctly calculated and that the number of values in the set of data is correctly identified in all examples and contexts.

The contexts of the lesson can be changed to reflect the interests of your pupils. The numbers chosen are designed to be manageable enough to maintain a focus on the calculation of the mean average. It is worth pointing out that the mean average value may well be different from any value in the set.

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).

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Starter quiz

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6 Questions

Q1.

What is the difference between 12 and 15?

Correct Answer: 3, three

Q2.

24 ÷ 6 =

Correct Answer: 4

Q3.

Match the equation to the answer.

Correct Answer:32 ÷ 8 = ,4

Correct Answer:54 ÷ 6 =,9

Correct Answer:35 ÷ 5 = ,7

Q4.

The data shows the number of pages read by four children. What is the mean average number of pages? Jun: 6; Sam: 5; Alex: 11; Jacob: 2

Correct answer: 6

Q5.

The data shows the number of pages read by four children. What is the mean average number of pages? Jun: 9; Sam: 0; Alex: 12; Jacob: 5

Correct answer: 6.5

Q6.

Lucas says: 'Sofia didn’t read anything so we can find the average pages read for all of us without her data.’ Is he correct?

Yes

Correct answer: No

Exit quiz

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6 Questions

Q1.

What is the missing mean average in the table? Can you reason about the missing value without doing the calculations again?

Correct answer: 7

Q2.

The table shows the number of cards each child currently has, the current total and mean average. Work out the mean average if Lucas gave one of his cards to Jun.

Correct Answer: 5

Q3.

The table shows the number of cards each child currently has, the current total and mean average. Work out the mean average if Aisha loses 5 of her cards.

Correct Answer: 4

Q4.

The table shows the number of cards each child currently has, the current total and mean average. Work out the mean average if Lucas gains an extra 10 cards.

Correct Answer: 7

Q5.

Six children are playing a card game. What total number of cards could the children have so that the mean average would be a whole number?

Correct answer: 36

Q6.

Some children play a card game. What number of cards could the children have so that the mean average would be a whole number when 4 or 5 of them are playing?

Correct answer: 20