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

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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.

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