|When a sample has been taken from a population, the data has to be analysed.
Different symbols are used for samples and populations.
Types of Data
An average is a number that represents the centre or central tendency of a set of data, or is typical of the sample.
The Mean of a Sample
The mean is commonly known by most people as the average.
The symbol used for the mean of a sample 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 in a frequency table, each score is multiplied by its frequency.
Finding the mean of a frequency distribution, including grouped data, is covered Topic 53, Statistical Graphs.
Findng the mean on a calculator
The procedure for finding statistical values will vary slightly from calculator to calculator.
For a typical scientific calculator, to find the mean of 5, 7, and 12:
Finding the mean on a spreadsheet
Enter the data:
The function entered in cell B5 to find the mean is =AVERAGE(A2..A4) this gives a mean of 8.
The median is the middle score or value when the data is arranged in order.
If there are an even number of scores, the median is halfway between the middle two values.
Finding the median from a set of data is covered further in the Spread topic.
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.
Finding Averages in a Frequency Distribution
The table shows the lengths of 100 possums caught in traps.
Mode The modal interval is the most common length which is 30 cm − 40 cm.
Median The median is midway between the 50th − 51st lengths which would be in the interval 30 cm − 40 cm.
Mean To find the approximate mean from a frequency table of grouped data the midpoint of each interval is multiplied by its frequency.
The approximate mean length of the 100 possums is 3050 ÷ 100 = 30.5 cm
Which average to use?
The Working with Data activity provides practice at finding the mean, median and mode.