What Does Average Mean?
Often when statistical results are shared, they showcase what the “average” value was. This can be confusing and sometimes deceptive since the “average” value could technically be 3 different values. These values are what we call the measures of central tendency.
A formal definition for a measure of central tendency is: it is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution.
There are 3 main measures of central tendency: the mode, the median, and the mean. We will consider the data set below when defining and explaining these three measures of central tendency:
Dataset: 1, 1, 2, 3, 3, 4, 4, 4, 5, 7
The mode is the most commonly occurring value in a distribution. In our data set, the mode is the number 4 because this is the number that occurs the most frequently.
The median is the middle value in the distribution. This will be the average of the two middle values if there are an even number of values, and it will be the middle value if there are an odd number of values. In our data set, the median is 3.5. We get this value by taking the average of the middle (5th & 6th) values, 3 and 4, by adding them together and dividing by 2 as follows: (4+3)/2=3.5.
The mean is the sum of the value of each observation in a data set divided by the total number of observations. In our data set, the mean is 3.4. We get this value by adding all the values together, which equals 34. Then we divide them by the total number of values in our data set, 10, to get our mean: 34/10=3.4.