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. http://www.stat.tamu.edu/~west/ph/meanmedian.html

Mound-shaped and symmetrical (Normal) Mean vs. Median Mound-shaped and symmetrical (Normal) Skewed Left Skewed Right 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.

Investigation 4: 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. What was the mean and median before the transfer joined the team? What was the mean and median after? Which one, for each situation, should you use as the measure of center? Explain. 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.)

Investigation 4: Mean vs. Median What was the mean and median before the transfer joined the team? Mean: ≈65.9 inches (≈5 ft 6 inches) Median: 66 inches (5 feet 6 inches) What was the mean and median after? Mean: ≈67.875 inches (≈5 ft 8 inches) Median: 66.5 inches (5 feet 6.5 inches) Which one, for each situation, should you use as the measure of center? Explain. Before: Either measure would be appropriate, no outliers After: Median, least effected by outliers 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.)

How do I know which measure of central tendency to use? Core plus comes after the PPT http://regentsprep.org/REgents/math/ALGEBRA/AD2/measure.htm