Averages

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 spread.

Determining averages (mean, median and mode)

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

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

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

To calculate the mean, add the numbers together and divide the total by the amount of numbers.

The mean for this example is:

\frac{{10 + 14 + 10 + 12 + 11 + 10 + 11 + 12 + 10 + 11 + 9 + 2}}{{11}} = \frac{{132}}{{11}} = 11

Question

A joiner bought 7 packets of nails. The number of nails in each packet was as follows:

8, 7, 6, 7, 9, 8, 7

Calculate the mean number of nails per packet. (Give your answer to 2 decimal places)

Total nails = 8 + 7 + 6 + 7 + 9 + 8 + 7 = 52

Number of packets = 7

Mean = \frac{52}{7}= 7.43

Finding the mean from a frequency table

Putting Kieran's results (data) into a frequency table looks like this.

Number of tracks on albumNumber of albums (Frequency)
91
104
113
123
130
141

We could have found the mean of his results by using this method

Number of tracks on albumFrequencyTracks x Frequency
919
10440
11333
12336
1300
14114
Total = 12Total = 132

When we divide these two totals as follows:

Mean = \frac{132}{12} = 11 tracks.