# Video: Using the Range to Find the Missing Value in a Set of Data

William has the following data: 6, 8, ๐, 8, 8, 9. If the range is 7, which number could ๐ be? [A] 5 [B] 6 [C] 9 [D] 2 [E] 8

02:12

### Video Transcript

William has the following data: six, eight, ๐, eight, eight, nine. If the range is seven, which number could ๐ be?

Weโre given five options with the values five, six, nine, two, or eight. Letโs start by reminding ourselves that the range of a set of data is the largest value subtract the smallest value. So if we look at our data set, ignoring ๐ for the time being, then the range can be found by our largest value, nine, subtract our smallest value, six, which is a range of three. This indicates that our unknown value ๐ must be larger or smaller than the existing values in the set.

So letโs take our value ๐ to be larger than the values in our set. Since weโre told that the range is seven, then the difference between our largest value ๐ and the smallest value of six must be seven. So six plus seven must equal ๐. So an answer for ๐ could be 13. But this answer isnโt given in our answer options. So letโs see if we can find the other potential value for ๐.

Here we would choose a value for ๐ thatโs smaller than the other values in our data set. Our range would still be seven. So the difference between ๐ and nine would be seven. In other words, ๐ plus seven equals nine. We can easily solve this to be ๐ equals two. And since two is given in option D, then we know that this is our final answer.

If we take a quick look at the other potential answers, we can see that the options of six, nine, and eight wouldnโt change the values in our set, meaning that the range would still be three. If we chose a value of ๐ equals five, then the range in this case would be nine take away five. Giving us four, which doesnโt fit with a range of seven and confirms our answer that ๐ must be two.