Objective 1: I Can Find the Mean, Median, and Mode of a Data Set

Statistics 2.3: Measures of Central Tendency

Objective 1: I can find the mean, median, and mode of a data set.

A ______is

The three most common ______are the ______, ______, and ______.

The ______of a data set is

*______is the summation symbol and is pronounced ______.

There are two variables to represent the mean. The population mean is represented by ______. The sample mean is represented by ______. N is the size of a ______n is the size of a ______

Read Example 1, pg 67

TIY 1: The ages of employees in a department are listed. What is the mean age? 34 27 50 45 41 37 24 57 40 38 62 44 39 40

The ______of a data set is the ______number of a data set once the numbers have been put in order from ______to ______. If there are two numbers in the ‘middle’, then the median is the ______of those numbers.

*True or False: You can find the mean and median for qualitative/nominal data sets. Explain why or why not.

Read Example 2 and Example 3, pg 68

TIY 2: The ages for a sample of fans at a rock concert are listed. Find the median age. 24 27 19 21 18 23 21 20 19 33 30 29 18 24 26 38 19 35 34 33 30 21 27 30 The ______of a data set is the value or values that appear the ______. There can be no mode if the data set does not have values that repeat. There can also be several modes if values repeat the same amount of times.

Read Example 4 and Example 5, pg 69

TIY 4: Find the mode of the ages of the residents of a nursing home. 88 72 83 87 72 91 85 79 77 87 90 80 76

TIY 5: In a survey, 240 US adults were asked if the US will ever have a female president. Of those surveyed, 171 responded “yes”, 45 responded “no” and 24 “didn’t know”. What is the mode?

An ______is a data value that is far removed from the other entries in the data set.

*The ______is most affected when there are outliers in the data set. In this case, it is best to use the ______to describe the ‘center’ of the data set.

Remember: Use the ______as the best measure of central tendency if there are no outliers. Use the ______as the best measure of central tendency if there are outliers. Use the ______as a measure of central tendency when the data is nominal.

Read Example 6, pg 70

TIY 6: Remove the data entry 65 from the data set in Example 6. Then find the mean, median, and mode. How does the absence of this outlier change each measure of central tendency?

Objective 2: I can find the weighted mean and grouped mean of a data set. Sometimes data sets contain entries that have a greater effect on the mean than other entries. The way your grade is found is an example of a ______. Summative assignments are worth four times more than formative assignments. So how do you calculate your ______? The formula to finding the ______is: Let’s look at a few easy examples using some student grades at Edsel. Example sheet, #1-4.

Pg 71, Example 7: You are taking a class in which your grade is determined from five sources: 50% from your test mean, 15% from your midterm, 20% from your final exam, 10% from your lab work, and 5% from your homework. Your scores are 86 (test mean), 82 (final exam), 96 (midterm), 98 (lab work), and 100 (homework). What is the weighted mean of your scores? If the minimum for an A is 90, did you get an A?

Extra Example: At a local college, the teachers with PhD's make $83,000, while the teachers with master's degrees make $67,000. If there are 12 PhD's and 24 master's degree teachers, find the mean salary for this group of teachers.

*Now let’s do examples 5 – 7 on the example sheet

If data are presented in a frequency distribution, that is called ______. How could you find the mean of data presented in a frequency distribution?

Class Frequency 1-3 12 4-6 7 7-9 9 10-12 3 Example 8: Use the frequency distribution below to approximate the number of minutes that a sample of Internet subscribers spend online during their most recent session.

TIY 8: Find the grouped mean of each data set.

Objective 3: I can determine the shape of a distribution. The graph of a frequency distribution can tell us a lot about the data. There are four types of shapes. 1) Symmetric 2) Uniform

3) Skewed left 4) Skewed right