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Problem 27 is a medium-level Pre-Algebra problem that could show up near the middle of an ACT
Math test. Take one minute to try to work this problem before viewing the solution.
The correct answer is E . This problem tests your knowledge of the definitions
of some statistics terms, median and mode. The median of a set of numbers is the one
right in the middle when the numbers are ordered from smallest to largest. The mode is the
number that shows up in the list most frequently.
To find the median we need to rewrite this list in order from smallest to largest. This
may seem like a waste of time, but I would not skip this step if I were working the problem,
because it's so easy to miss a number and make a mistake. I like to rewrite the numbers
one by one, crossing them off as I go to make sure I don't miss any.
The smallest is 75, cross that off, then 77, 78, 80, 86, 86 again, and the largest number
is 92. That's our list, from smallest to largest.
For the median, we look for the number right in the middle, and that would be 80. If we'd
had an even number of numbers, there'd be two numbers in the middle, and in that case
we'd have to average those two numbers to get the median. But in this problem there
are 7 numbers, so there is a number right in the middle and it's 80.
The mode is the number that shows up the most often. Sometimes the mode doesn't exist, like
when none of the numbers in the list repeats. But in this case we have one number that repeats,
86, it shows up twice. The mode is 86. So we have a median equal to 80 and a mode equal
to 86, choice E.
Mean, Median, and Mode kind of go together since they are all related to statistics.
Getting one of these problems right is usually just a matter of knowing the definitions.
For a list of N numbers: The Mean, also called the average, is the
sum of numbers divided by N. We've already used this definition in a previous problem.
The Median is the middle value when the list is ordered. You can do the ordering smallest
to largest OR largest to smallest and the median will still be right in the middle.
The Mode is the most frequently occurring number.
Here's one way to remember these definitions: The first thing I think of when I hear the
word median is that strip down the MIDDLE of a highway. The median is the MIDDLE number
in an ordered list. To remember the definition for MODE, notice
that the word MOST sounds a lot like the word MODE. The MODE is the number that shows up
the MOST.