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Measures of centre

Calculate and interpret the mean, median and mode of datasets, including finding the mean from a frequency table and choosing the most appropriate measure for a given context.

Worked examples

Finding the mean of a dataset

Straightforward

Problem

Find the mean of the dataset: 5, 8, 3, 10, 45, \ 8, \ 3, \ 10, \ 4.

Finding the median and mode

Moderate

Problem

For the dataset 7, 3, 9, 3, 5, 11, 3, 87, \ 3, \ 9, \ 3, \ 5, \ 11, \ 3, \ 8, find (a) the median and (b) the mode.

Finding the mean from a frequency table

Challenging

Problem

The frequency table below shows the number of siblings reported by 2020 students.

Number of siblingsFrequency05182433\begin{array}{|c|c|}\hline \text{Number of siblings} & \text{Frequency} \\ \hline 0 & 5 \\ 1 & 8 \\ 2 & 4 \\ 3 & 3 \\ \hline \end{array}


Find the mean number of siblings.

Practise

Q1·Straightforward
Find the mean of the dataset: 3, 7, 5, 9, 63, \ 7, \ 5, \ 9, \ 6.
Q2·Straightforward
Find the mean of the dataset: 12, 15, 11, 14, 1312, \ 15, \ 11, \ 14, \ 13.
Q3·Straightforward
Find the mean of the dataset: 4, 8, 6, 24, \ 8, \ 6, \ 2.
Q4·Straightforward
Find the mean of the dataset: 8, 10, 12, 14, 168, \ 10, \ 12, \ 14, \ 16.
Q5·Moderate
Find the median of the dataset: 2, 9, 5, 7, 32, \ 9, \ 5, \ 7, \ 3.
Q6·Moderate
Find the median of the dataset: 4, 8, 2, 10, 6, 144, \ 8, \ 2, \ 10, \ 6, \ 14.
Q7·Moderate
Find the mode of the dataset: 3, 5, 3, 7, 9, 5, 3, 13, \ 5, \ 3, \ 7, \ 9, \ 5, \ 3, \ 1.
Q8·Moderate
Find the median of the dataset: 15, 9, 22, 18, 31, 22, 15, 2215, \ 9, \ 22, \ 18, \ 31, \ 22, \ 15, \ 22.
Q9·Challenging
The frequency table below shows the number of pets owned by students in a class.

Number of petsFrequency12243341\begin{array}{|c|c|}\hline \text{Number of pets} & \text{Frequency} \\ \hline 1 & 2 \\ 2 & 4 \\ 3 & 3 \\ 4 & 1 \\ \hline \end{array}


Find the mean number of pets. Give your answer to one decimal place.
Q10·Challenging
The frequency table below shows the scores students received on a quiz.

ScoreFrequency436483\begin{array}{|c|c|}\hline \text{Score} & \text{Frequency} \\ \hline 4 & 3 \\ 6 & 4 \\ 8 & 3 \\ \hline \end{array}


Find the mean score.
Q11·Challenging
Nine students score between 6060 and 8080 on a test, but one student scores 55. Which measure of centre best represents the typical score?
Q12·Challenging
The frequency table below shows the number of goals scored per game by a football team over a season.

GoalsFrequency0315263442\begin{array}{|c|c|}\hline \text{Goals} & \text{Frequency} \\ \hline 0 & 3 \\ 1 & 5 \\ 2 & 6 \\ 3 & 4 \\ 4 & 2 \\ \hline \end{array}


Find the mean number of goals per game. Give your answer to one decimal place.