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New
Year 10
Higher

Weighted means

I can calculate and compare weighted means.

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New
New
Year 10
Higher

Weighted means

I can calculate and compare weighted means.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. There may be cases where one value has more weight (importance).
  2. The weighted mean takes this into account.
  3. The percent weight given to each value is called a weighting factor.

Common misconception

That for all situations the weightings are subjective.

There are situations in which a subjective decision is made about weightings but there are also situations where the multipliers used are dictated by the context in a logical way. An example of this is combining groups and combining their means.

Keywords

  • Weighting factor - A weighting factor is a multiplier used to reflect the importance of a piece (or pieces) of data relative to the rest of the data.

  • Weighted mean - A weighted mean is the mean calculated for a set of data where weighting factors have been applied.

Consider extending the activity in the third learning cycle. Either with drawing (or with something else) decide on a few different criteria that it can be judged by and then let pupils decide on their individual weightings for those criteria. Pupils could draw (or nominate) items to be compared.
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.
The sum of the 5 data points in a data set is 200. The mean of this data set is .
Correct Answer: 40
Q2.
8 people bought a mean of 3 loaves of bread. The total number of loaves of bread that were bought is loaves.
Correct Answer: 24, 24 loaves, 24 loaves of bread
Q3.
12 people used a mean of 2.5 litres of water. The total amount of water that was used is litres.
Correct Answer: 30, 30 litres
Q4.
In group A, 3 people spent a mean of £4. In group B, 5 people spent a mean of £6. How much money, in total, was spent altogether across both groups A and B?
£5
£10
£15
Correct answer: £42
£360
Q5.
In total, how many people are there in this data set?
An image in a quiz
Correct Answer: 98, 98 people
Q6.
An estate agent records the number of rooms in each flat in a block of flats. The mean number of rooms is correct to 2 decimal places.
An image in a quiz
Correct Answer: 5.15, 5.15 rooms

Exit quiz

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6 Questions

Q1.
Which of these statements defines a weighting factor when referring to a weighted mean?
The mass of a factor
The mean mass of a factor
Correct answer: A multiplier used to show the importance of a data point
An additive value used to show the importance of a data point
Q2.
In group A, 6 people have a mean score of 10. In group B, 4 people have a mean score of 12. The mean score of everyone in groups A and B combined is .
Correct Answer: 10.8
Q3.
In group A, 2 earn a mean of £200 per day. In group B, 3 earn a mean of £180 per day. In group C, 5 earn a mean of £250 per day. The mean amount earned by all 10 people is £ .
Correct Answer: 219, £219, 219.00, £219.00
Q4.
Alex takes an art course. The two coursework tasks and final exam have weightings depending on how long the assignment is. The sum of all three values in the $$s\times f$$ column is .
An image in a quiz
Correct Answer: 533
Q5.
An interview consists of two tasks, each with a different importance. Which of these calculations finds the weighted mean for this data set?
An image in a quiz
$$711\over2$$
Correct answer: $$711\over15$$
$$130\over2$$
$$130\over15$$
$$130-15$$
Q6.
A social media influencer reviews a meal at a restaurant and weights the criteria of price, taste, and presentation in the ratio 2 : 1 : 7. Their weighted rating (out of 10) for this meal is .
An image in a quiz
Correct Answer: 4.4