## Averages When a sample has been taken, the data has to be analysed.
An average is a number that represents or is typical of the sample.
Three types of average are commonly used: the mean, the median and the mode.

### The Mean

The mean is commonly known by most people as the average.

The symbol used for the mean is .

The mean is calculated by adding together all of the scores or values and dividing by the number of scores or values. If the data is grouped together in a frequency table, the middle score of each group or class is used. )

### The Median

The median is the middle score or value when the data is arranged in order.

If there are an even number of scores, take half way between the middle two values.

### The Mode

The mode is the most common score or value.

If all of the scores are different there is no mode.

If the data is grouped together in a frequency table, the group with highest frequency is called the modal group or class.

 Examples Answer For the following set of test results of 10 people: 3, 8, 5, 6, 8, 5, 4, 1, 10, 5 Find: (a) The mean (b) The mode (c) The median (a) The mean (b) The mode = 5 (occurs 3 times) (c) Arrange in order: 1, 3, 4, 5, 5, 5, 6, 8, 8, 10 Median is 5

### Which average to use?

 Average Advantage Disadvantage mean Uses all of the values. Can be found easily on a calculator. Influenced by extreme high or low values. e.g. 5, 5, 6, 7, 8, 9, 100Mean is 140÷7 =20  The value of 100 has a big effect on the mean. median Not influenced by extreme high or low values. e.g. 4, 5, 6, 7, 8, 9, 100The value of 100 does not effect the median. Hard to work out if there are a large number of values. mode Good for finding the most popular value. e.g. Finding the most popular pizza size. May not be all that representative of a set of values. e.g. 3, 3, 4, 5, 6, 8, 9, 10, 12.The mode is 3 which is not near the middle.

The Working with Data activity provides practice at finding the mean, median and mode.