The scores 5, 6, 6, 7, 46 have a mean of 14. Which describes a typical score better, the mean or the median? Why?

The median, 6, because the outlier 46 pulls the mean up

Free worksheet · Australian Curriculum

Mean, median and mode worksheets with answers

Three ways to describe a typical value, and the range to describe the spread. Learn when each one is useful, then practise with fresh questions and worked solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Mean, median, mode and range, explained

How to find each one, including the cases that trip students up.

1. The mean: add, then divide

Add all the values, then divide by how many there are. For 4, 8, 6, 5, 7:

$\text{mean} = \frac{4 + 8 + 6 + 5 + 7}{5} = \frac{30}{5} = 6$

2. The median: put them in order first

The median is the middle value once the data is in order. For 3, 9, 4, 7, 5, order it as 3, 4, 5, 7, 9, so the median is $5$ .

With an even number of values, the median is halfway between the middle two. For 2, 5, 8, 10 the median is $\dfrac{5 + 8}{2} = 6.5$ .

3. The mode: the most common value

For 3, 5, 5, 6, 8, 8, 8 the mode is $8$ . A data set can have two modes (bimodal) or no mode at all, if every value appears the same number of times.

4. The range: highest minus lowest

The range measures spread, not a typical value. For 3, 5, 5, 6, 8, 8, 8 the range is $8 - 3 = 5$ .

5. Outliers pull the mean, not the median

For 4, 5, 5, 6, 50 the mean is $\dfrac{70}{5} = 14$ , but the median is $5$ . One very large value dragged the mean up, so the median describes a typical value better here.

6. Finding a missing value from the mean

Work with the total. The mean of five numbers is $7$ , so their total is $5 \times 7 = 35$ . If four of them are $5, 8, 6$ and $9$ (total $28$ ), the fifth is

$35 - 28 = 7$

Quick check: 10 questions

Try each one, then open the answer.

Find the mean of 2, 4, 6, 8, 10.
Answer
$6$
Find the median of 7, 1, 5, 3, 9.
Answer
$5$
Find the median of 12, 15, 18, 20.
Answer
$16.5$
Find the mode of 4, 7, 7, 2, 9, 7, 4.
Answer
$7$
Find the range of 15, 3, 22, 9, 11.
Answer
$19$
Find the mean of 3.5, 4.5, 6, 8.
Answer
$5.5$
Find the mean, median and mode of 2, 3, 3, 5, 7, 10.
Answer
Mean $5$ , median $4$ , mode $3$
A student's mean score over 6 tests is $72$ . What is the total of the 6 scores?
Answer
$432$
The mean of four numbers is $15$ . Three of them are $12$ , $18$ and $10$ . Find the fourth.
Answer
$60 - 40 = 20$
The scores 5, 6, 6, 7, 46 have a mean of $14$ . Which describes a typical score better, the mean or the median? Why?
Answer
The median, $6$ , because the outlier $46$ pulls the mean up

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Questions

What is the difference between mean, median and mode?

The mean is the total divided by the number of values, the median is the middle value in order, and the mode is the most common value. All three describe a typical value in different ways.

How do you find the median of an even number of values?

Put the values in order and find the two in the middle. The median is halfway between them: add them and divide by 2.

When is the median better than the mean?

When the data has an outlier or is skewed. One very large or very small value moves the mean a lot but barely moves the median.

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