To draw conclusions from data, it is useful to calculate averages. An average indicates the typical value of a set of data and the main types are mean, median and mode. You can also get more information from your data by giving a measure of central tendency and a measure of spread.

Example

As part of a school project, Kieran is asked to write down the number of tracks on each of his CDs. His results are as follows:

10, 14, 10, 12, 10, 11, 12, 10, 11, 9 and 12.

This gives Kieran the information he needs, but the data is not very easy to read or remember. What can he do to improve on this? One way is to put his results into a table:

The mean

The mean is the most common measure of average. If you ask someone to find the average, this is the method they are likely to use.

Kieran's results were:

10  14  10  12  10  11  12  10  11  9  12

To calculate the mean:

Add the numbers together and divide the total by the amount of numbers.

The mean for this example is:

Kieran only had 11 results, so calculating the mean in this way was not too time consuming or complicated.

Finding the mean from a frequency table

If Kieran had 111 CDs, it is likely that he would have made a mistake while typing the results into his calculator. In cases like this, finding the mean from a frequency table is more efficient.

Work through an example in the activity below to practise reading information from a frequency table.

The median

The median is the middle number. To calculate the median of any set of numbers, you need to write the numbers in order.

To find the median number:

• Put all the numbers in numerical order.
• If there is an odd number of results, the median is the middle number.
• If there is an even number of results, the median will be the mean of the two central numbers.

Finding the median with an odd number of results

Using the same example, find the median number of tracks on Kieran's CDs.

Kieran's results were:

10  14  10  12  10  11  12  10  11  9  12

• Put the numbers in numerical order:
• 9  10  10  10  10  11  11  12  12  12  14

• Find the middle number:
• 9  10  10  10  10  11  11  12  12  12  14

The middle number is 11, so the median is 11.

Finding the median with an even number of results

To find the median of the numbers: 5  11  12  4  8  21.

• Put the results in order:
• 4  5  8  11  12  21.

• Find the middle number or numbers:
• 4  5  8  11  12  21.

If there are two central numbers, we need to find their mean.

The median is therefore:

(8 + 11) ÷ 2 = 9.5

Finding the median from a frequency table

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