Question Video: Determining the Effect of Removing a Data Input on the Range of a Data Set Mathematics • 6th Grade

The table shows the amount of money Liam saves each day. Describe how the range would change if the data for Thursday was not included.

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Video Transcript

The table shows the amount of money Liam saves each day. Describe how the range would change if the data for Thursday was not included.

In this table, we’re given six days of the week, along with a savings amount for each day. For example, on Saturday, Liam saves four dollars and 92 cents. We’re asked to work out how the range would change if the data for Thursday was not included. So let’s have a look.

We can remember that the range of a set of data is calculated as the highest data value subtract the lowest data value. If we look at the table, the highest value here occurs on Wednesday. It’s 13 dollars and 46 cents. The lowest value is four dollars and eight cents, which he saves on a Tuesday. We therefore need to calculate 13 dollars and 46 cents subtract four dollars and eight cents. When we work this out, we get a range of 9.38 or nine dollars and 38 cents. So what would happen if we didn’t include the data for Thursday?

Let’s cover it up and see what happens when we take the highest value subtract the smallest value. Well, the highest value is still going to be 13 dollars and 46 cents. And the lowest value is the same. It’s still four dollars and eight cents. And so even when we don’t include Thursday, we still get the same range. In fact, we could’ve removed the amounts for Saturday, Sunday, or Monday as well and it still wouldn’t have affected the range. The range would only be affected if we didn’t include the highest or the lowest data value.

We can therefore give a statement for the answer, something like the range would remain unchanged at 9.38 or nine dollars and 38 cents.

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