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.

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

Weighted means

Maths

Checking understanding of summary statistics from a list

Checking understanding of summary statistics from a frequency table

Calculating summary statistics from a grouped frequency table

Calculating the mean from a grouped frequency table

Constructing stem and leaf diagrams

Calculating summary statistics from stem and leaf diagrams

Checking understanding of measures of central tendency

Comparing data sets in context

Statistical summaries using technology

Comparing various representations of data sets

Problem solving with comparisons of numerical data

In this unit, pupils began to compare two different sets of data. In the future unit, pupils will consider cumulative frequency graphs and histograms and compare the data from these diagrams to other graphical representations.

In the prior unit, pupils considered the mean, median and mode and evaluated their usefulness in a variety of contexts. In this unit, pupils extend this learning to comparing two different data sets and comparing these measures of central tendency.

In this unit pupils will compare two different data sets and compare different measures of central tendancy when interpreting the data. Pupils will learn to interrogate frequency tables and stem and leaf diagrams both with and without technology.

Comparisons of numerical summaries of data

A multiplier used to show the importance of a data point

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

Which of these statements defines a weighting factor when referring to a weighted mean?

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 {{ }}. 

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 £{{ }}.

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

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 {{ }}.

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

8 people bought a mean of 3 loaves of bread. The total number of loaves of bread that were bought is {{ }} loaves.

12 people used a mean of 2.5 litres of water. The total amount of water that was used is {{ }} litres.

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?

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

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.

Weighted means

Lesson outcome