Sec. 2.3 Measures of Central Tendency Mr. Ricks Madison High School

Measures of Central Tendency A measure of central tendency is a value that represents a typical, or central, entry of a data set Mean, median, and mode are three common ways this is reported

What do you Mean?

Don’t cross the Median! The median is the “center” of a sorted data set If there is an odd number of entries, the median is the middle entry If there is an even number of entries, the median is the average of the 2 middle entries Qualitative data sets will not have a mean or median

Math a la “Mode” The mode describes the entry that occurs most frequently in a data set If no entry is repeated there is no mode If 2 entries occur with the same greatest frequency the data set is bimodal Qualitative data sets can have a mode An outlier is a data point that is far removed from the other entries in the data set Outliers can skew the central tendencies in a set

Find the mean, median, and mode By hand Calculator Which better describes the center of this data set, the mean or median? Why?

The ages of the students in Billy Madison’s 3 rd grade class are 8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,10,10,27 Find the mean, median, and mode. How would these values change if Billy wasn’t in the class?

College Algebra Test Data Find the mean, median, and mode Is the mean or median a better description for the center? Why?

100 students were asked about Avengers:Age of Ultron OpinionFrequency It was awesome47 It was ok28 It was disappointing15 Never saw it10 How would we find the mean, median, and mode for this data set?

Distribution Shapes Symmetric if both halves of graph are very similar Uniform if all bars are approximately the same height Skewed-left if tail extends to the left Skewed-right if tail extends to the right

Symmetric Chart Uniform Chart The mean works well to describe the central tendency for these distributions

Skewed Left Chart Skewed Right Chart Median is best to describe the center of a skewed distribution.

Bimodal Chart

What is the Distribution? Activity Work with your team One piece of paper per team Answer the questions together for each scenario Be prepared to discuss with the class

Assignment Pg. 64# 1-3,5-14, odd (only part a), 29,30,39-42 (26 problems)