1. What is the typical value?
Measures of Center
What is the typical value?
These definitions are a little more student friendly than the ones in C-MAPP and are OK to use. The ones in C-MAPP are more precise.
How to find: 1.)
2.)
Write in notes

2. Measures of Center cont’d
These definitions are a little more student friendly than the ones in C-MAPP and are OK to use. The ones in C-MAPP are more precise.
How to find: 1.)
2.)
Write in notes

3. The Formula Write in notes! Discuss what symbols mean!
x-bar is the symbol for the mean of the
is the capital Greek letter sigma, which stands for “sum.”
x is an individual data value
n is the number of data values.
Note: Students do NOT need to memorize this formula. They need to know, use, and be able to describe the process for finding the mean.
Write in notes!

4. Mean vs. Median http://www.stat.tamu.edu/~west/ph/meanmedian.html
Let’s look at how outliers affect the placement of the mean and the median relative to the distribution. Use the applet to explore the effect of outliers on the mean and the median.

5. How do I know which measure of central tendency to use?
Write in notes

6. Mean vs. Median
Ask them to discuss with a shoulder buddy where the mean and median for each distribution would be located. They should make a quick sketch on their paper and mark where these values would be.
What is the location of the mean relative to the median in each type of distribution? Why does this happen?
In a symmetrical distribution, the mean and the median are approximately equal. In skewed distributions, the outliers tend to “pull” the mean towards them, in order to maintain the mean as a balance point for the data set.

7. Here are Max’s quiz grades in his common core class:
84, 81, 80, 75, 80, 88, 84, 83, 84, 85, 90, 78
What is the mean?
What is the median?
How do these numbers compare? Are there any outliers?
82.7
83.5
Not very different at all (both C)…no outliers
Write in notes!

8. Grades continued…
Max forgot to come to tutorial for the 1st quarter so he is getting a 0 for that grade. Add this grade onto the list and answer the same questions:
What is the mean?
What is the median?
How do these numbers compare? Are there any outliers?
76.3 83
Substantially different (dropped down to a D for the average)…yes
Write in notes!

9. Discussion
Which number would you rather use? In reality…which number would your grade really be? Thoughts on outliers? COME TO TUTORIAL!!!
Don’t write in notes

10. Investigation: Mean vs. Median
The heights of Washington High School’s basketball players are: 5 ft 9in, 5 ft 4in, 5 ft 7 in, 5ft 6 in, 5 ft 5 in, 5 ft 3 in, and 5 ft 7 in. A student transfers to Washington High and joins the basketball team. Her height is 6 ft 10in. -Find the mean and median of the data. In complete sentences, state the statistics and determine which measure should be used to describe the height of the team.
Discuss and solve in your groups!
Let’s talk about the mean vs. the median. How do you know which one to use? Consider this situation:
Read the problem, then give groups time to answer the questions on the worksheet. Discuss answers.
What is the mean height of the team before the new player transfers in? (65.9 in.) What is the median height? (66 in.)
What is the mean height after the new player transfers? (67.9 in.) What is the median height? (66.5 in.)
What effect does her height have on the team’s measures of center? (The mean increased by 2 in. and the median increased by .5 in.)
How many players are taller than the new mean team height? (2) How many players are taller than the new median team height? (4)
Which measure of center more accurately describes the team’s typical height? Explain. (The median gives a more accurate description of the team’s typical height. Half of the players are taller than the median (and half shorter) but only two players are taller than the mean. Using the mean would lead someone to conclude that the team is taller than they really are.)

11. Where did they go wrong??
Mean: 75 Median: 87 Outlier: 25 Max: 97 Min: 25 The distribution of the data is fairly symmetric with a center of around 75. There is an outlier of 25 and range of 72. Based on the statistics above, what is incorrect about the description of the data and why?

12. Ticket out the Door
What happens to the mean of a data set when you add one or more data values that are outliers? Explain.
What happens to the mean of a data set when you add values that cluster near one end of the original data set? Explain.
Explain why you think these changes might occur.