Calculating Averages (the Mean, Median and Mode)

Calculating averages is a remarkably important skill. It is taught to and is essential for a wide range of people; ranging from students, business people and obviously statisticians. Calculating an average such as the mean, median or mode allows a person to give a fair representation to a set of data.

For the examples which I am about to conduct I will use the below figures:

1, 5, 6, 7, 2, 3, 4, 9, 10, 8, 10

Mean

Calculating the mean is a very quick, effective and widely used method of gaining an average from a set of data. It can be done in 3 very easy steps.

General formula:

"Mean = (x)/n"

Step 1: Add up all of the numbers (in the formula these will be our "x" values.)

1+5+6+7+2+3+4+9+10+8+9+10= 55 (Therefore 55 is x)

Step 2: Count the total amount of numbers.

There are 11 separate values in our example (thus n=11 in our formula).

Step 3: Divide the answer from Step 1 by Step 2.

55 / 11 = 5 (Therefore our mean is 5!)

Notes:

a) The mean does not always have to be an integer. There may be decimals and recurring decimals in your final answer. The significant figures or decimal places to which you give your answers are generally personal preference unless stated otherwise (in an exam question for example).

b) Be careful with zero-values. They do not contribute to the x, although they still count when tallying up the value of "n".

Mode

Calculating the mode is by far the simplest of all three averages to calculate and is exceptionally easy to get a grip on. The mode is simply the most commonly occurring value within the set of values.

In our set of values this would be 10.

As a more effective way to calculate the mode a person may wish to place his/her numbers in order. Our list of values would now look like this:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10

This makes it a bit easier to find which of our values is the most common and if using computer programmes such as Excel the hard work can be done for you when calculating this average.

Notes:

a) When handling very small or very large sets of data ordering the numbers may not be time effective.

b) Mode will require you to browse through and keep a tally of the times a value has occurred, thus it may be unsuitable for a person who has a large piece of data to manage.

c) The mode must always be a value that has occurred within your data, and thus can only be a decimal should one appear within the set of data.

Median

In my personal experience median

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