11.1.1 Calculating the Mean of a Data Set

You have probably come across the mean before; it is the most commonly used type of average and takes into account all the data.

Let’s look at an example to explore this type of average.

Suppose eight students took an exam, with the following scores:

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To get a feel for the problem and to help you check that your final answer is reasonable, look at the exam scores and decide what a typical value might be. Make a note of your estimate.

To calculate the mean value, we add all the data values together and then divide this sum by the number of values.

In this example, the sum of the data values is sum with, 8 , summands nine plus seven plus six plus seven plus eight plus four plus three plus nine equals 53.

There are eight data values. Therefore, the mean value is 53 divided by eight equals 6.625.

The mean exam score for these students was 6.6 (rounded to 1 decimal place).

How did this compare with the typical value you estimated at the beginning? Did you decide that 6 or 7 might be a typical value?

The mean value will always lie between the smallest value and the largest value, and will often be somewhere towards the middle, though exactly where depends on the actual values in the data set.

Calculating the Mean

Calculating a mean can be summarized as follows:

  • Add all the values together to find their sum.
  • Count the number of values.
  • Divide the sum by the number of values.
  • Write down the conclusion and include the units.

Alternatively, mean value equation left hand side equals right hand side sum of values divided by number of values.

Remember to make a note of this in your math notebook for easy reference later.

Adobe PDF IconTake a look at this pencast to see how to calculate the mean.

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Solution symbolActivity: Finding the Mean Time for a Trip

Here’s an example for you to try. The times for my trip to work during one week last month are shown in the table below:

Commute Times

Day of Week Monday Tuesday Wednesday Thursday Friday
Time in Minutes 42 58 45 47 52

First, look at the data. What would you say is a typical length of time for the trip from this set of data? Write down your estimate.

Now calculate the mean commute time using the method given above.

Solution symbol

Answer

The smallest time is 42 minutes and the largest is 58 minutes, so a typical time would lie between these, perhaps 50 minutes. Your estimate may be different from this, of course, because it is just a sensible guess at a typical value.

To calculate the mean:

The sum of the values is sum with, 5 , summands 42 plus 58 plus 45 plus 47 plus 52 equals 244.

There are five data values, so the mean is 244 minutes divided by five equals 48.8 minutes.

The mean commute time over that week was about 49 minutes.

Remember to include the units. In this case, the units are minutes.

The mean is fairly close to the estimated typical value of 50 minutes, so it looks as if the calculated value for the mean is correct.

11.1.2 Using a Calculator to Find the Mean