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There are all kinds of tools to describe and compare data.
If we want to take a look at the central tendency of a set of data,
three common tools are the mean, the median and the mode.
The mean is what you are probably used to just calling the average.
And
to find the average of any set of data
you just add up the numbers that are in that set and then you divide by how many numbers are in the set.
So let's take an example.
Suppose that we have a 10 point quiz
and the results from this ten point quiz are a seven and nine
a six, a nine and a seven.
Well, if we'd like to find the mean of this set of data
were going to
add up all of these numbers:
seven plus nine
plus six
plus nine
plus seven.
And we're going to divide by how many numbers there are. 12345
Remember that the division bar is a grouping symbol, so we have to add the numbers in the numerator before we do
any division. And we'll get
38 divided by five
which is in mean of 7.6
So that is
one measure of central tendency of the set of data.
Another one which is commonly used is the median.
Median is the number that's in the exact middle of a set of data when the data is arranged from low to high.
So let's take our set of data here and let's arrange it from low and high. We have six
and seven
and seven
then nine
and then nine.
When we take a look at this
6979
the seven is in the exact middle, so the median in this particular case
is the score seven. You notice we have one mean and we have one median.
The last measure is called the mode.
And the mode is
the data element that is
most commonly occurring.
You can have one mode or two and you can have sets of data that are multimodal. In this particular set of data
we have two modes
because
both seven and nine appear twice.
Lets take a look at another example.
Again suppose that we have
a 10 point quiz and now the scores on this
quiz for a different set of students is 7, 9
two
six
10 and eight.
Let's find a mean that the median and the mode for this set of data.
So for the mean we're going to
add up all of these scores. Seven plus nine plus two
plus six
plus 10 and plus eight
divided by how many 123456 items.
Remembered to add the numerator first, we get
42 divided by six. That means that are mean for the set of data is seven.
Let's find the median and again we're going half to arrange the data
in order.
Let's arrange it from low to high...
two
six
seven
eight
nine
and 10.
Now when we want to find
the number that's exactly in the middle, we can start counting off from the ends, but if you notice
we don't have a single number in the middle because we have an even number of data elements.
We've got two in the middle. So what we do?