1. Section 3.1 Measures of Center HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.

2. A measure of central tendency describes a central, or typical, value in a data set. The mean, median, and mode are all measures of central tendency. Numerical Descriptions of Data 3.1 Measures of Center HAWKES LEARNING SYSTEMS math courseware specialists

3. The mean is what we typically call the “average” of a data set. To calculate the mean, simply add all the values and divide by the total number in the data set. Formula: Calculating the Mean: HAWKES LEARNING SYSTEMS math courseware specialists It is possible for the mean not to be a number in the data set. Numerical Descriptions of Data 3.1 Measures of Center

4. 63 68 71 67 63 72 66 67 70 Calculate the sample mean of the following heights in inches: HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center Solution: When calculating the mean, round to one more decimal place than what is given in the data.

5. The median is the middle value in an ordered set. To calculate the median, first put the numbers in numerical order. Then, a.if n is odd, the median is the number in the center. b.if n is even, the median is the mean of the center two numbers. Calculating the median: HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center It is possible for the median not to be a number in the data set.

6. a.15 16 11 22 19 10 17 22 Calculate the median of the following sets of data: HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center Solution: 10 11 15 16 17 19 22 22 b.2.6 3.3 5.0 1.8 0.7 2.2 4.1 6.1 6.7 Solution: 0.7 1.8 2.2 2.6 3.3 4.1 5.0 6.1 6.7

7. The mode is the data value(s) that occur(s) most frequently. A data set may have one mode (unimodal), two modes (bimodal), or many modes (multimodal). If each data value occurs the same number of times, then there is no mode. Calculating the mode: HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center The mode will always be a number in the data set.

8. a.63 68 71 67 63 72 66 67 70 Calculate the mode of each data set: HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center Solution: 63 68 71 67 63 72 66 67 70 b.51 77 54 51 68 70 54 65 51 Solution: 51 77 54 51 68 70 54 65 51 c.1 5 7 3 2 0 4 6 Solution: No mode

9. This all depends on the data: For qualitative data, the mode should be used. For quantitative date, the mean should be used unless the data set contains outliers. Quantitative data sets with outliers should use the median. Which measure of the “average” is the best to use? HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center

10. Choose the best measure of center for the following data sets: HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center a.The average t-shirt size (S, M, L, XL) of American women. Mode b.The average salary for a professional team of baseball players. c.The average price of houses in a subdivision of similar houses. Mean Median