# 11.1.2 Using a Calculator to Find the Mean

The calculator can be accessed on the left-hand side bar under Toolkit.

In the last activity, you were asked to calculate the mean of the following commute times:

## Commute Times

Day of Week | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|

Time in Minutes | 42 | 58 | 45 | 47 | 52 |

A student used the calculator to work out the mean in one step—can you spot anything that is not correct with how they did this?

The key sequence used was:

## Activity: Using a Calculator to Find the Mean

Enter the student’s key sequence above into the calculator.

(a) Write down the answer given and explain how you know that the answer is incorrect.

### Answer

(a) The answer given is 202.4. You know this is incorrect because it is much larger than all of the values. The mean value will always be between the smallest and largest values. You may also have said that it does not correspond to our previous answer which is another good way to check the calculator answer.

(b) Where did the student make a mistake?

### Answer

(b) The student should have divided the sum of the values by the number of values. Remember the order of operations (PEDMAS), which we discussed in detail in Unit 4. As division takes precedence over addition, the calculator has divided 52 by 5 to get 10.4 and then added that to the first four numbers. Did you spot this when you looked at the key sequence?

(c) Write down two calculator sequences that could be used to calculate the mean correctly.

### Answer

(c) Brackets can be used to calculate the sum before the division. The key sequence is:

Alternatively, the sum can be calculated by pressing the equals sign before the division is carried out, then dividing the sum by the appropriate value.

The key sequence is:

Use the calculator to check that these two sequences give the correct answer.

When you are calculating a mean value, remember to check that it lies between the smallest and largest values in the data set. And remember to include the units, too!

In this example, the mean commute time is again 48.8 minutes, which is the same as our previous answer now!

Here’s a fun game [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] that lets you see how changing values affects the mean.

11.1.1 Calculating the Mean of a Data Set