The average in Math is also often referred to as the mean. The average value that this page focuses on is the “arithmetic average” or “arithmetic mean”.
There are other averages that can be worked out when finding the average in Math, such as the weighted average and geometric average.
But the word “average” or “mean” when used on this page, will refer specifically to the arithmetic average, unless stated otherwise.
Arithmetic Average,
Calculating an Average
When calculating an average of a set/group of data values, what we do is we add up the data values together,
then divide this amount by the number of data values there are in the set/group.
So looking at a random list of 5 numbers: 11 , 14 , 6 , 21 , 8.
\bf{\frac{11 \space + \space 14 \space + \space 6 \space + \space 21 \space + \space 8}{5}} = \bf{\frac{60}{5}} = 12
Meaning if we picked out any number at random from this group of 4, we would likely expect the value to probably be near to 14.
Although, 6 and 21 are a bit more apart from this mean value.
There are often certain outliers in data sets.
Finding the Average in Math Example
Shown below is a data frequency table showing values for how many minutes a group of 18 people spend preparing their lunch.
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In order to find the mean/average amount of minutes a person spent preparing lunch.
We can help firstly by adding a third column, which will display the total amount of minutes spent preparing lunch by each individual group combined.
We can then add up all the minutes together, and then divide this amount by the number of people studied, 18.
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Now to calculate the average, we divide 141 minutes by the 18 people.
\bf{\frac{141}{18}} = 7.83The average or mean amount of time by the people preparing lunch is 7.83 minutes.
Calculating an Average, Outliers
With average values, something that we should often watch out for in a set/group of data is what can be referred to as “outliers”.
Outliers are certain values in a group of data that are seen to be fairly far away from most of the other values, these outliers can be either higher or lower.
For example we could have a list of the top speeds of different cars.
190mph can be seen to be an outlier here.
The mean/average top speed is:
\bf{\frac{140 \space + \space 144 \space + \space 150 \space + \space 145 \space + \space 143 \space + \space 190}{6}} = \bf{\frac{912}{6}} = 152mph
The outlier value of 190mph raises the mean/average of the group.
But without 190mph:
Mean/average = \bf{\frac{140 \space + \space 144 \space + \space 150 \space + \space 145 \space + \space 143}{5}} = \bf{\frac{720}{5}} = 144.4mph
144mph is an average value that is a more reasonable mean/average top speed for the group.
Sometimes, it can be a useful idea to leave out certain outliers in some situations, when trying to calculate an average.
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