When you have completed this chapter, you will be able to: Explain the concept of central tendency, identify and compute the arithmetic mean, compute and interpret the weighted mean, determine the median, identify the mode, explain and apply measures of dispersion, compute and explain the variance and the standard deviation. | Describing Data: Numerical Measures Chapter 03 Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin LEARNING OBJECTIVES LO3-1 Explain the concept of central tendency. LO3-2 Identify and compute the arithmetic mean. LO3-3 Compute and interpret the weighted mean. LO3-4 Determine the median. LO3-5 Identify the mode. LO3-6 Explain and apply measures of dispersion. LO3-7 Compute and explain the variance and the standard deviation. LO 3-8 Explain Chebyshev’s Theorem and the Empirical Rule. 3- Parameter vs. Statistics PARAMETER A measurable characteristic of a population. STATISTIC A measurable characteristic of a sample. 3- Sample Mean LO 3-2 Identify and compute the arithmetic mean. 3- Weighted Mean The weighted mean of a set of numbers X1, X2, ., Xn, with corresponding weights w1, w2, .,wn, is computed from the following formula: LO 3-3 Compute and interpret the weighted mean. The Carter Construction Company pays its hourly employees $, $, or $ per hour. There are 26 hourly employees, 14 of whom are paid at the $ rate, 10 at the $ rate, and 2 at the $ rate. What is the mean hourly rate paid the 26 employees? 3- The Median PROPERTIES OF THE MEDIAN There is a unique median for each data set. Not affected by extremely large or small values and is therefore a valuable measure of central tendency when such values occur. Can be computed for ratio-level, interval-level, and ordinal-level data. Can be computed for an open-ended frequency distribution if the median does not lie in an open-ended class. EXAMPLES: MEDIAN The midpoint of the values after they have been ordered from the smallest to the largest, or the largest to the smallest. The ages for a sample of five college students are: 21, 25, 19, 20, 22 Arranging the data in ascending order gives: 19, 20, 21, 22, 25. Thus the median is 21. The heights of four basketball players, in inches, are: 76, 73, 80, 75 . | Describing Data: Numerical Measures Chapter 03 Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin LEARNING OBJECTIVES LO3-1 Explain the concept of central tendency. LO3-2 Identify and compute the arithmetic mean. LO3-3 Compute and interpret the weighted mean. LO3-4 Determine the median. LO3-5 Identify the mode. LO3-6 Explain and apply measures of dispersion. LO3-7 Compute and explain the variance and the standard deviation. LO 3-8 Explain Chebyshev’s Theorem and the Empirical Rule. 3- Parameter vs. Statistics PARAMETER A measurable characteristic of a population. STATISTIC A measurable characteristic of a sample. 3- Sample Mean LO 3-2 Identify and compute the arithmetic mean. 3- Weighted Mean The weighted mean of a set of numbers X1, X2, ., Xn, with corresponding weights w1, w2, .,wn, is computed from the following formula: LO 3-3 Compute and interpret the weighted mean. The Carter Construction Company pays its .
