Stat_Chapter 3 Key Words

Stat_Chapter 3 Key Words - 1 Chapter 3 Descriptive Measures...

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1 Chapter 3: Descriptive Measures Statistics 211: Tu-Th, 9/13-15/2011 3.1 Measures of Center Mean of a Data Set (with single variable) – sum of the observations divided by the number of observations Median of a Data Set (with single variable) – the middle of the data set; if odd then middle of the ordered list; if even then the average or mean or the two middle points Mode of a Data Set – a value that occurs more than once or greatest frequency; if does not occur more than once then no mode Comparison of Mean, Median and Mode Mean = Sum of Observations No. of Observations Median = Middle Value in Ordered List Mode = Most frequent value Where (relative positions) do mean and median fall in right skewed, symmetric or left skewed? Resistant Measure – sensitive to influence of a few extreme observations; median is a resistant measure of center; but the mean is not. Why? Trimmed Mean – removing portion of extreme values before calculating average Examples when to use Mean (test scores), Median (Real Estate Price), Mode (Boston Marathon Runners) Sample Mean x g3364 = ∑ g3025 g3284 g3041 Test Score Example: Sum or X i = X 1 + X 2 + X 3 + X 4 = 88 + 75 + 95 + 100 = 358/4 = 89.5 average test score 3.2 Measures of Variation Range of Data Set – distance between smallest and largest endpoint values of data set Range = Maximum value – Minimum Value Sample Standard Deviation – how far on average the observations are from the mean
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2 Deviations from the Mean - Example Height Deviation from the Mean Standard Deviation x x – g2206g3365 ______________________( x – g2206g3365 ) 2 ______ 72 -3 0 73 -2 4 76 1 1 76 1 1 78 3 9 24 Sum of Squared Deviations – subtract mean from each observation; then square each value Sample Variance g1871 g2870 = ∑ ( g3051 g3284 g3051̅ ) g3118 g3041 g2879 g2869 = 24/5-1 = 6 (dividing by n-1 because estimating sample variance from population variance) Sample Standard Deviation – Defining Formula how far on average the observations in the sample are from the mean of the sample (square root of standard deviation) s = g3495∑ ( g3051 g3284 g2879g3051̅ ) g2870 g3041g2879g2869 = 6 = 2.4 inches height of starting players Example Starting Height of Players (Example No. 2): 67, 72, 76, 76, 84 Step 1: Compute Mean x g3364 = ∑ g3025 g3284 g3041 = 75 inches Step 2: Construct table to obtain sum or squared deviations = 156 Step 3: Calculate sample standard deviation s = g3495∑ ( g3051 g3284 g2879g3051̅ ) g2870 g3041g2879g2869 = g3493 156/4 = 6.2 Heights of the players vary from the mean of 75 inches by 6.2
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