Measures of Central Tendency 10-3 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

Measures of Central Tendency10-3

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpOrder the values from least to greatest.

1. 9, 4, 8, 7, 6, 8, 5, 3, 7

2. 36, 22, 35, 46, 37, 47, 30

Divide.

3. 4.

3, 4, 5, 6, 7, 7, 8, 8, 9

22, 30, 35, 36, 37, 46, 47

661983

5764

144


Problem of the Day

A mom buys a white, a green, a blue, and a yellow sweater for her 4 children. Bill and Bob refuse to wear yellow. Barb doesn’t like green, and Beth hates green and white. Mom will not put the boys in white, and Bob wont wear blue. Which sweater will each child wear? Barb:iwhite, Beth:iyellow,

Bob:igreen, Bill:iblue


MA.8.S.3.2 Determine and describe how changes in data values impact measures of central tendency.

Sunshine State Standards


Vocabulary

meanmedianmoderangeoutlier


Measure of central tendency are used to describe the middle of a data set. Mean, median, and mode are measures of central tendency.


An outlier is a value that is either far less than or far greater than the rest of the values in the data.


21, 21, 28, 29, 51, 28, 32

Additional Example 1: Analyzing the Effects of Outliers

Identify the outlier in the data set, and determine how the outlier affects the mean, median, mode, and the range of the data set.


21, 21, 28, 29, 51, 28, 32

mean: 21 + 21 + 28 + 29 + 28 + 32 = 159 Add the values.

Divide by 6, the number of values.1596

= 26.5

median: 21 21 28 28 29 32 Order the values.

mode: Two values occur twice.

The median is 28.

21, 28

Additional Example 1 Continued

range: 32 – 21 = 11

The outlier is 51. This value is much greater than the others.

Without the outlier:


21, 21, 28, 29, 51, 28, 32

mean: 21 + 21 + 28 + 29 + 51 + 28 + 32 = 210 Add the values.

Divide by 7, the number of values.2107

= 30

median: 21 21 28 28 29 32 51 Order the values.

mode: Two values occur twice.

The median is 28.

21, 28

Additional Example 1 Continued

range: 51 – 21 = 30

The outlier is 51. This value is much greater than the others.

With the outlier:


21, 21, 28, 29, 51, 28, 32Additional Example 1 Continued

The outlier increases the mean by 3.5 and the range by 19. It has no effect on the median or modes.


4, 12, 7, 5, 20, 9

Check It Out: Example 1A

Identify the outlier in the data set, and determine how the outlier affects the mean, median, mode, and range of the data.


4, 12, 7, 5, 20, 9

Check It Out: Example 1A Continued

The outlier is 20. It increases the mean by 2.1, the median by 1, and the range by 8. It has no effect on the mode (still no mode).


15, 19, 20, 15, 2, 11

Check It Out: Example 1B

The outlier is 2. It decreases the mean by 2.4 and increases the range by 9. It has no effect on the median or the mode.


Additional Example 2: Analyzing the Effect of Changing Data

A market researcher asked students which of a list of products they were likely to buy. The results are shown below.

How are the mean, median, and mode percent of interested students affected if further research shows that 32% of the students said they would buy a sixth product, Product F?

Product Percent of students willing to buy

Product A 48%

Product B 25%

Product C 32%

Product D 42%

Product E 19%


Find the mean, median, and mode of percent of students willing to buy five products and then those willing to buy six products. Compare the results.

mean: 48 + 25 + 32 + 42 + 19 5

= 33.2

median: 19, 25, 32, 42, 48

mode: 19, 25, 32, 42, 48

There is no mode.

Percent willing to buy 5 products:

The median is 32.

The mean is 33.2



mean: 48 + 25 + 32 + 42 + 19 + 32 6

= 33

median: 19, 25, 32, 32, 42, 48

mode: 19, 25, 32, 32, 42, 48

The mode is 32.

Percent willing to buy 6 products:

The median is 32.

The mean is 33.32 + 32

2= 32

Including the percent of student interest in Product F decreased the mean by 33.2 – 33 = 0.2%, did not change the median, and resulted in the data now having a mode of 32.




A market researcher asked students which of a list of products they were likely to buy. The results are shown below.

How are the mean, median, and mode percent of interested students affected if further research shows that 15% of the students said they would buy a sixth product, Product F?

Product Percent of students willing to buy

Product A 21%

Product B 33%

Product C 10%

Product D 50%

Product E 9%


Suppose the market researcher in Example 2 wants to know only about student interest in Products A–D. How would the mean percent of interest change from when all six Products A–F were considered?

Check It Out: Example 2

This mean is an increase of 36.75 – 33 = 3.75% in student interest from when all 6 products were included.

= = 36.7548 + 25 + 32 + 424

1474

The mean now includes only 4 products.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Measures of Central Tendency10-3Lesson Quiz

Use the data to find each answer.

1. Identify the outlier in the data set and determine how the outlier affects the mean, median, mode, and range of the data.

2. Which measure of central tendency would make the scores in Game 3 seem the highest?

3. What is the value of the measure you chose Problem 2?

38; the outlier decreases the mean by 12.5 and the median by 0.5. It increases the range by 121 and has no effect on the mode.

median

171.5


1. Use the data given below to identify the mean of the science test scores.

A. 80

B. 85

C. 89

D. 92



2. Use the data given below to identify the mode of the science test scores.

A. 85

B. 90

C. 85, 90

D. no mode



3. Use the data given below to identify the median of all the scores.

A. 21

B. 15

C. 14

D. 12


Documents

Measures of Central Tendency 10-3 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes