Weighted means | Maths | Quizalize & Oak National Academy

Starter quiz

The sum of the 5 data points in a data set is 200. The mean of this data set is ______.

'40' ✓
8 people bought a mean of 3 loaves of bread. The total number of loaves of bread that were bought is ______ loaves.

'24' ✓
12 people used a mean of 2.5 litres of water. The total amount of water that was used is ______ litres.

'30' ✓
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

£42 ✓

£360
In total, how many people are there in this data set?

'98' ✓
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.

'5.15' ✓

Exit quiz

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

A multiplier used to show the importance of a data point ✓

An additive value used to show the importance of a data point
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 ______.

'10.8' ✓
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 £______.

'219' ✓
$Alex takes an art course. The two coursework tasks and final exam have weightings depending on how long the assignment is. The sum of all three values in the <Math>s\times f</Math> column is <span class="blank">______</span>.$

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 ______.

'533' ✓
An interview consists of two tasks, each with a different importance. Which of these calculations finds the weighted mean for this data set?

$711\over2$

$711\over15$ ✓

$130\over2$

$130\over15$

$130-15$
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 ______.

'4.4' ✓

Worksheet

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Lesson Details

Key learning points

There may be cases where one value has more weight (importance).
The weighted mean takes this into account.
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.