MATH 112 Section 7.2: Measuring Distribution, Center, and Spread

Measures of Center

Measures of Spread

Distributions

Conclusion

MATH 112 Section 7.2: Measuring Distribution, Center, and

Spread

Prof. Jonathan Duncan

Walla Walla College

Fall Quarter, 2006

Measures of Center

Outline

Measures of Spread

1 Measures of Center The Arithmetic Mean The Geometric Mean The Median The Mode

2 Measures of Spread

3 Distributions

4 Conclusion

Distributions

Conclusion

Measures of Center

Measures of Spread

Distributions

Conclusion

Analyzing Data

In the last section we focused on presenting an overall picture of data using tables or graphs. Now we will examine ways to analyze certain characteristics of data such as the data set's center, spread, and distribution.

Example

In your first year as a teacher, you and another teacher both give the same test to your classes of 25 children. The two classes have the following scores:

Your Class 93 92 92 90 87 85 84 80 79 78 77 76 75 74 71 71 71 71 71 70 68 66 62 59 53

Other Class 98 98 97 95 94 93 89 88 87 84 82 77 76 72 71 70 65 64 63 61 61 60 58 58 47

Measures of Center

Measures of Spread

The Arithmetic Mean

Defining the Arithmetic Mean

Distributions

Conclusion

If you wanted one number to capture your classes' performance, what would it be?

Arithmetic Mean The arithmetic mean is found by adding all numbers in the data set and dividing by the number of values in the data set.

Example

Your Class:

53+59+???+92+93 25

75.8

Other Class:

47+58+???+98+98 25

76.4

Based on these numbers, which class did better? Is the arithmetic mean an accurate summary of the exam scores?

Measures of Center

Measures of Spread

The Arithmetic Mean

The Arithmetic Mean and Outliers

Distributions

Conclusion

There are some issues to keep in mind when using the arithmetic mean. One of these issues is the effect of outliers?data points which are much smaller or larger than the typical value.

Example

A new student transfers into your class and scores 100% on the test. How does this affect the mean score?

The arithmetic mean changes from 75.8 to 76.7.

Example One of the students in your class who scored a 71 on the exam is found to have cheated and their score is changed to a zero. How does this affect your mean score?

The arithmetic mean changes from 75.8 to 73.0.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download