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## Other measures of spread

# Range and mid-range

## Video transcript

Find the range and the
mid-range of the following sets of numbers. So what the range tells us is
essentially how spread apart these numbers are, and
the way you calculate it is that you just
take the difference between the largest
of these numbers and the smallest
of these numbers. And so if we look at the
largest of these numbers, I'll circle it in magenta,
it looks like it is 94. 94 is larger than
every other number here, so that's the
largest of the numbers. And from that, we
want to subtract the smallest of the numbers. And the smallest of the numbers
in our set right over here is 65. So you want to
subtract 65 from 94. And this is equal to-- Let's
see, if this was 95 minus 65, it would be 30. 94 is one less than
that, so it is 29. So the larger this number is,
that means the more spread out. The larger the difference
between the largest and the smallest number. The smaller this is, that means
the tighter the range, just to use the word itself, of
the numbers actually are. So that's the range. The mid-range is
one way of thinking to some degree of kind of
central tendency, so mid-range. And what you do
with the mid-range is you take the average of the
largest number and the smallest number. So here we took the difference. That's the range. The mid-range would be the
average of these two numbers. So it would be 94 plus 65. And when I talk
about average, I'm talking about the
arithmetic mean over 2. So this is going to be what? 90 plus 60 is 150. 150, 4 plus 5 is 159. 159 divided by 2 is equal
to-- 150 divided by 2 is 75. 9 divided by 2 is 4 and 1/2. So this would be 79.5. So it's one kind
of way of thinking about the middle
of these numbers. Another way is obviously
the arithmetic mean, where you actually take
the arithmetic mean of everything here. Obviously, you could
also look at things like the median and the mode. So range and mid-range.