Chapter 3 - Describing data: Numerical measures. Learning objectives of this chapter include: Calculate the arithmetic mean, weighted mean, median, mode, and geometric mean; explain the characteristics, uses, advantages, and disadvantages of each measure of location; identify the position of the mean, median, and mode for both symmetric and skewed distributions; compute and interpret the range, mean deviation, variance, and 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 .
