### Measures of Central Tendency

Grab a pair of headphones and check out the quick introductory video below.

#### Introduction video from Mr. Townsley

The measure of central tendency you're probably most familiar with is the mean.  The mean is also known as the average.  To find the mean, add up all of the data and divide by the number of entries.  Check out the "mean" formulas on p. 67 of your textbook and add them to your study guide.

Another measure of central tendency you may be familiar with is the median.  The median is the value that lies in the middle of the data when the data set is ordered.  If there are an odd number of entries in a data set, finding the median is pretty easy:
10 11 15 20 24
15 is the median of the data set above because it is the middle number.

Check out the video here to learn more about the median when there is an even number of entries in the data set.

Yet another measure of central tendency is the mode.  The mode of a data set is the data entry that occurs with the greatest frequency.  It is possible for a data set to have more than one mode (if there are two modes, then a data set is called bimodal) and it is also possible for a data set to have no mode.

An outlier is a data entry that is far removed from the other entries in the data set.  Here's an example:
The following numbers are the amount of dollars a person typically spends on coffee each day on his/her way to work.
\$2.50 \$3.50 \$2.75 \$1.99 \$3.75 \$1.95 \$2.63 \$3.28 \$10.17 \$2.78

Which one is the outlier?  You guessed it!  \$10.17.  This number is fairly far removed from the rest of the entries. You might be thinking to yourself right now, "okay, Mr. Townsley...how far does the datum actually need to be away from the rest of the numbers in order for it to be considered an outlier?  I mean, would \$7.89 have been an outlier?  What about \$9.19?"  That's a really good question.  Statisticians don't always agree on what makes something an outlier.  We'll talk more about this later on in our course.

Weighted Mean
Plenty of classes at SHS use "weighted grades."  Have you ever wondered how weighted grades work?  It seems strange that you could be getting all of the homework points but not do well on the tests and still be failing a class.  This class uses weighted grades.
Homework, projects & quizzes: 15%
Tests:                                         70%
Cumulative Test:                        15%

Let's assume you got all of the homework points (100%), had earned 85% on the tests and didn't do so well on the final...an abysmal 60%.  What would you overall course grade be?  If you didn't know anything about weighted means/grades, you might think that adding 100%, 85% and 60% and then dividing by three (three categories) would be the way to figure out your grade.  100+85+65 = 250.      250/3 = 83 1/3%
Since the grades are weighted, the 100% homework grade (weighted at 15%) needs to count for less of your overall grade than the tests you took (weighted at 70%).  The weighted grade calculation should look like this:

weight x score
HW         .15 x 100 = 15
Tests        .70 x 85 =59.5
Cum Test .15 x 60 = 9

Add them up.  15 + 59.5 + 9 = 83.5%   It's a little bit better than you thought!

Check out the video here to make some more sense of weighted means.  Be sure to write down the formula for weighted mean in your study guide found on p. 71 of your textbook.

Mean of a Frequency Distribution
Yesterday in class, we organized large numbers of data into frequency distributions.  To find the mean of a data set already arranged into a frequency distribution is a lot like finding a weighted mean.  Write down the steps for finding the mean of a frequency distribution (it might help to write the formula down, too) from p. 72 in your study guide.  To see an example worked out, check out the video here.

Practice! Find the mean of the frequency distribution we created in our study guide yesterday.  Add this to the appropriate place in your study guide.  Check with a few of your classmates to see if they agree with the mean you calculated.

The Shape of Distributions
When a data set is graphed using a frequency histogram, statisticians look at the "shape."  Check out p. 73 in your textbook.  Take a few notes in your study guide about the different shapes of distributions.  Be sure to read about how the shape of a data set influences the position of the mean, median and mode.  For another explanation of this connection, check out the website here or the applet here.

That's it!  After completing the feedback form below, please work on your assignment.