Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Chapter 3 Descriptive Statistics: Numerical Methods

3-2 Chapter Outline 3.1Describing Central Tendency 3.2Measures of Variation 3.3Percentiles, Quartiles and Box-and-Whiskers Displays 3.4Covariance, Correlation, and the Least Square Line (Optional) 3.5Weighted Means and Grouped Data (Optional) 3.6The Geometric Mean (Optional)

Describing Central Tendency In addition to describing the shape of a distribution, want to describe the data set’s central tendency A measure of central tendency represents the center or middle of the data May or may not be a typical value LO 3-1: Compute and interpret the mean, median, and mode.

3-4 Measures of Central Tendency Mean,  The average or expected value Median, M d The value of the middle point of the ordered measurements Mode, M o The most frequent value LO3-1

Measures of Variation Figure 3.13 LO 3-2: Compute and interpret the range, variance, and standard deviation.

3-6 Measures of Variation RangeLargest minus the smallest measurement VarianceThe average of the squared deviations of all the population measurements from the population mean StandardThe square root of the Deviation variance LO3-2

3-7 The Empirical Rule for Normal Populations Figure 3.14 LO 3-3: Use the Empirical Rule and Chebyshev’s Theorem to describe variation.

3-8 z Scores For any x in a population or sample, the associated z score is The z score is the number of standard deviations that x is from the mean A positive z score is for x above the mean A negative z score is for x below the mean The mean has a z score of zero LO3-3

Percentiles, Quartiles, and Box-and-Whiskers Displays For a set of measurements arranged in increasing order, the p th percentile is a value such that p percent of the measurements fall at or below the value and (100-p) percent of the measurements fall at or above the value The first quartile Q 1 is the 25 th percentile The second quartile (or median) is the 50 th percentile The third quartile Q 3 is the 75 th percentile The interquartile range IQR is Q 3 - Q 1 LO 3-4: Compute and interpret percentiles, quartiles, and box- and-whiskers displays.

Covariance, Correlation, and the Least Squares Line (Optional) A positive covariance indicates a positive linear relationship between x and y As x increases, y increases A negative covariance indicates a negative linear relationship between x and y As x increases, y decreases LO 5: Compute and interpret covariance, correlation, and the least squares line (Optional).

3-11 Correlation Coefficient Magnitude of covariance does not indicate the strength of the relationship Correlation coefficient (r) is a measure of the strength of the relationship that does not depend on the magnitude of the data LO3-5

Weighted Means and Grouped Data (Optional) Sometimes, some measurements are more important than others Assign numerical “weights” to the data Weights measure relative importance of the value LO 3-6: Compute and interpret weighted means and the mean and standard deviation of grouped data (Optional).

The Geometric Mean (Optional) For rates of return of an investment, use the geometric mean Suppose the rates of return are R 1, R 2, …, R n for periods 1, 2, …, n The mean of all these returns is the calculated as the geometric mean: LO 3-7: Compute and interpret the geometric mean (Optional).