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Measures of Central Tendency and Dispersion MM2D1 Using sample data, students will make informal inferences about population means and standard deviations... a. Understand and calculate the means and standard deviations of sets of data. b. Use means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution. Central Tendency Measure of Central Tendency- a number used to represent the center or middle of a set of data values. MEAN-average Shown as x with a line---- and read “x-bar.” MODE-most often, may be one, none, or more than one MEDIAN-(think of a road) middle when written in numerical order. Could be the average of the middle two if there is an even number of terms. Mean, Median, Mode The test scores received by students on a history exam are listed below. Which measure of central tendency best represents the data? 65, 68, 71, 77, 82, 86, 88, 93, 95, 97 Mean, Median, Mode 65, 68, 71, 77, 82, 86, 88, 93, 95, 97 Mean-82 Mode-93 Median-84 Mean and median represent best. Mode is greater than the rest of the data. Measures of Dispersion Disperse-to spread out Range-greatest minus the least Standard Deviation (σ-read “sigma”) Measures of Dispersion Checkpoint In a golf tournament, the top 6 men’s scores are given. Compare the mean and standard deviation of the set of scores. Men’s: 65, 68, 70, 72, 73, 75 Measures of Dispersion Checkpoint Men’s mean 70.5 Men’s standard deviation Square root(65-70.5)2+(68-70.5)2+……. Square root 6 Square root of 65.5 6 =3.3 Try your samples Personal project Choose one of the following numbers to collect: Your grades from the last 6 grades. The weights of 6 of your peers. The number of siblings of each member of the class. The number of hours you study each night –Monday-Friday Find the mean, median, mode, range, and standard deviation of your choice. Report it to the class by presentation.