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

Michael has the following data: 6, 8, 𝑘, 8, 8, 9. If the range is 3, which number could 𝑘 be? [A] 3 [B] 4 [C] 5 [D] 6 [E] 13

03:15

Video Transcript

Michael has the following data: Six, eight, 𝑘, eight, eight, and nine. If the range is three, which number could 𝑘 be? Is it (A) three, (B) four, (C) five, (D) six, or (E) 13?

We recall that we can calculate the range by subtracting the smallest value from the largest value. In this question, we will consider what the largest value and smallest values are when 𝑘 takes each of the five options. One of these options will have a range of three which will be the correct answer. When 𝑘 is equal to three, our list of values in ascending order are three, six, eight, eight, eight, and nine. As the largest value is nine and the smallest value is three, the range will be equal to nine minus three. As this is equal to six, option (A) is not correct.

When 𝑘 is equal to four, the smallest value is four and the largest value is nine. This time the range would be equal to nine minus four, which is equal to five. Once again, this is not correct. When 𝑘 is equal to five the smallest number is five. The largest number is still nine. The range in this case is equal to four, which once again is not correct. When 𝑘 is equal to six, we have two sixes. We could write these in either order. Our list is now six, six, eight, eight, eight, and nine. As the smallest number in this set of date of is six and the largest is nine, the range is equal to nine minus six. This is equal to three, which suggests that option (D) is correct.

We will check option (E) just to make sure. This time, 𝑘 is equal to 13. This means that the smallest number is six and the largest number is 13. The range is the difference between these values. 13 minus six is equal to seven. So this answer is also incorrect. This means that the correct answer is option (D). If the range is three, the number from the list that 𝑘 could be is six.

There are a few other numbers that were not one of the options that 𝑘 could be. As long as six remains the smallest number and nine remains the largest number, the range will always be three. This means that 𝑘 could be any one of the four integers, six, seven, eight, or nine. In this question, the only one of those that was listed as an option was six, which is why this is the only correct answer.

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