Video Transcript
Jennifer has the following data:
10, eight, seven, nine, and 𝑚. If the median is eight, which
number could 𝑚 be? Is it (A) seven, (B) 8.5, (C) nine,
(D) 9.5, or (E) 10?
The median represents the middle of
the data. This means that half of the data
values are above it and half are below it. We can start by putting the data in
order and thinking about how we can work out the number 𝑚. Writing the four values that we
know in order gives us seven, eight, nine, and 10. We are told that the median is
eight. As the median is the middle of five
values, it must be the third number when listed in order from lowest to highest. There must be two values above
eight and two values below eight. For the number to be written to the
left of eight, it must be less than or equal to eight.
If 𝑚 was any integer value less
than seven, it would be the first number in the list. Positive integers here could be
one, two, three, four, five, and six. None of these are options in the
question, though. The missing number could also be
seven as both the sevens would be written to the left-hand side of eight as they are
less than eight. Out of our five options, the
correct answer is option (A), seven. 𝑚 could not be 8.5, nine, 9.5, or
10 as all of these are greater than eight and would be on the right-hand side of
eight.
It is possible that the missing
number could’ve been eight. If this was the case, seven would
be the first number in our list. We would then have two eights. The third number would still be
eight, which is the median. Whilst the value of 𝑚 could be any
number less than or equal to eight, the correct answer in this case is seven.
