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

The mean, median, and mode are all measures of central tendency. HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center 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.

The mean is what we typically call the “average” of a data set. HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center Calculating the Mean: 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: It is possible for the mean not to be a number in the data set.

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

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

HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center Calculate the median of the following sets of data: 15 16 11 22 19 10 17 22 Solution: 10 11 15 16 17 19 22 22 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

The mode is the data value(s) that occur(s) most frequently. HAWKES LEARNING SYSTEMS math courseware specialists Numerical Descriptions of Data 3.1 Measures of Center Calculating the mode: 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 only once, then there is no mode. The mode will always be a number in the data set.

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

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

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

Average = (12 + 9 + 7 + 13 + 2 + 11) ÷ 6 Average = 54 ÷ 6 Average = 9

Order = (2 7 9 11 12 13) Median = (9 + 11) ÷ 2 Median = 10

Average = [(16*4) + (17*3) + (17*0)] ÷ (16 + 17 + 17)