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MEASURES OF CENTER TENDENCY AND DISPERSION Kayla Gonzalez Miranda Arce Gabriela Loriga Oscar Bardinas Emmanuel Cortes MEASURES OF CENTRAL TENDENCY AND OUTLIERS o One way to summarize a set of data is to use a measure of central tendency. Mean, median, and mode are all measures of central tendency. o The measure of central tendency that best describes a data set may depend on whether the data set has an outlier. o An outlier is a data value that is much greater or less than the other values in the set. MEAN, MEDIAN, AND MODE o The mean equals sum of the data values total number of data values oUse mean to describe the middle of a set of data that does not have an outlier. o The median is the middle value in a data set when the values are arranged in order. For a set containing an even number of data values, the median is the mean of the two middle data values. o Use median to describe the middle of a set of data that does have an outlier. o The mode is the data item that occurs the most amount of times. A data set can have no mode, one mode, or more than one mode. o Use mode when the data are nonnumeric or when choosing the most popular item. MEAN, MEDIAN, AND MODE Practice Problem 1 What are the mean median and mode of the bowling score below? Which measure of central tendency best describes the scores? Bowler 1 2 3 4 5 6 7 8 Score 104 117 104 136 189 109 113 104 Mean: Median: Mode: MEAN, MEDIAN, AND MODE Practice Problem 2 Your grades on three exams are 80, 93, and 91. What grade do you need on the next exam to have an average of 90 on the four exams? MEASURE OF DISPERSION AND RANGE OF A SET OF DATA o A measure of dispersion describes how dispersed, or spread out, the values in a data set are. o One measure of dispersion is range. o The range of a set of data is the difference between the greatest and least data values. MEASURE OF DISPERSION AND RANGE OF A SET OF DATA Practice Problem 3 Number of Weekly Sales The pie chart on the right shows the numbers of weekly sales a salesperson made in the first nine weeks of a ten-week sales period. The salesperson’s target is an average of 14 sales each week. How many sales does the sales person need in the tenth week to meet the target average? 12(1) 14(3) 13(2) 15(3)