### 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.