### Mean

Finding the mean is the same as being asked to find the average.

To find the mean of a set of numbers you can follow this simple method::

- Add up all the numbers to find the
__total__. - Count how many numbers there are.
- Divide the
__total__by how many numbers there are.

Let’s work through an example question.

Example

Whilst looking through my telescope at nearby galaxies I record the number of shooting stars I see in each galaxy:

7, 10, 2, 4, 7, 11, 14, 9

What is the mean number of shooting stars in a galaxy?

First we just add up the values:

7 + 10 + 2 + 4 + 7 + 11 + 14 + 9 = __64__

Next we count how many numbers there are:

‘7’ = 1, ’10’ = 2, ‘2’ = 3, ‘4’ = 4, ‘7’ = 5, ’11’ = 6, ’14’ = 7, ‘9’ = __8__

Then we divide the total by how many numbers there are:

64 ÷ 8 = 8

So the mean number of shooting stars in a galaxy is **8**.

### Median

The median value is the middle value.

The median value sits right in the middle if you line all your values up in size order.

To find the median value folow this method:

- Line all the numbers up in size order.
- Find the middle number in the list – this is the median number.
- If there are two numbers in the middle of the list (because the list has an even number of values) the median is halfway between these two middle numbers.

Let’s work through an example question together.

Example

Here are some shopping items and their prices:

- Cosmic cabbage – £3
- Venusian Steak – £21
- Moon Cheese – £9
- Wormhole soup – £4
- Fiery rocket – £2
- Solar salad – £5
- Sputnik sprouts – £2

What is the median price of these items?

First we arrange them in size order:

£2 £2 £3 £4 £5 £9 £21

Then we find the middle number, as there are 7 items in this list the middle number is the 4th one.

The median number is this middle number:

£4

If £4 had not been in the list in this example question the answer would actually still have been £4. Why? Because without £4 in the list there would be two middle values, £3 and £5 and the median is halfway between the two, which is £4.

### Mode

The mode (or modal value) is the one that occurs the most often.

To find the modal value you simply count the number of times each value occurs. The one that occurs most often is the mode.

Here’s an example question:

Example

Over 10 weeks I recorded the number of aliens who visited earth:

- Week 1 – 3
- Week 2 – 4
- Week 3 – 8
- Week 4 – 5
- Week 5 – 3
- Week 6 – 8
- Week 7 – 2
- Week 8 – 3
- Week 9 – 4
- Week 10 – 2

What is the modal number of aliens visiting earth each week?

We need to count the number of times each number is recorded. A good way to do this is to make a quick tally chart, or a simple list and record the number of times each value occurs with ticks or tallies:

3: ✓✓✓

4: ✓✓

8: ✓✓

5: ✓

2: ✓✓

Now we can see that the modal number, the one that occurs most often, is 3.

### Range

The range is the difference between the biggest value and the smallest value.

You work out the range by putting all the values in order. Then subtract the smallest value from the biggest one. Easy!

Let’s work through an example question.

Example

Here is a line graph showing the average temperature recorded on each day in a week:

What is the temperature range in the graph?

So first we find the lowest temperature, it is on Tuesday, it is:

4°C

Next we find the highest temperature, it is on Sunday, it is:

29°C

Then we subtract the lowest temperature from the highest:

29 – 4 = 25°C

So the temperature range is **25°C**.