Essentials of Modern Business Statistics 7 e Anderson

Essentials of Modern Business Statistics (7 e) Anderson, Sweeney, Williams, Camm, Cochran © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 1

Essentials of Modern Business Statistics (7 e) Chapter 3, Part A Descriptive Statistics: Numerical Measures q Measures of Location q Measures of Variability © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 2

Essentials of Modern Business Statistics (7 e) Numerical Measures § If the measures are computed for data from a sample, they are called sample statistics. § If the measures are computed for data from a population, they are called population parameters. § A sample statistic is referred to as the point estimator of the corresponding population parameter. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 3

Essentials of Modern Business Statistics (7 e) Measures of Location q q q q Mean Median Mode Weighted Mean Geometric Mean Percentiles Quartiles © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 4

Essentials of Modern Business Statistics (7 e) Mean § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 5

Essentials of Modern Business Statistics (7 e) § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 6

Essentials of Modern Business Statistics (7 e) Population Mean m § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 7

Essentials of Modern Business Statistics (7 e) Example: Monthly Starting Salary A placement office wants to know the average starting salary of business graduates. Monthly starting salaries for a sample of 12 business school graduates is provided here. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 8

Essentials of Modern Business Statistics (7 e) § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 9

Essentials of Modern Business Statistics (7 e) Median § The median of a data set is the value in the middle when the data items are arranged in ascending order. § Whenever a data set has extreme values, median is the preferred measure of central location. § The median is the measure of location most often reported for annual income and property value data. § A few extremely large incomes or property values can inflate the mean. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 10

Essentials of Modern Business Statistics (7 e) Median For an odd number of observations: 7 observations 26 12 14 18 18 27 19 12 26 14 27 27 19 27 In ascending order Median is the middle value Median = 19 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 11

Essentials of Modern Business Statistics (7 e) Median For an even number of observations: 8 observations 26 18 27 12 14 27 19 30 12 14 18 19 26 27 27 30 In ascending order Median is the average of the middle two values. Median = (19 + 26)/2 = 22. 5 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 12

Essentials of Modern Business Statistics (7 e) Median Example: Monthly Starting Salary Averaging the 6 th and 7 th data values: Median = (3, 890+ 3, 920)/2 = 3, 905 Note: The data is in ascending order Monthly Starting Salary ($) 3, 710 3, 755 3, 850 3, 880 3, 890 3, 920 3, 940 3, 950 4, 050 4, 130 4, 325 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 13

Essentials of Modern Business Statistics (7 e) Trimmed Mean § Another measure sometimes used when extreme values are present, is the trimmed mean. § It is obtained by deleting a percentage of the smallest and largest values from a data set and then computing the mean of the remaining values. § For example, the 5% trimmed mean is obtained by removing the smallest 5% and the largest 5% of the data values and then computing the mean of the remaining values. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 14

Essentials of Modern Business Statistics (7 e) Mode § The mode of a data set is the value that occurs with greatest frequency. § The greatest frequency can occur at two or more different values. § If the data have exactly two modes, the data are bimodal. § If the data have more than two modes, the data are multimodal. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 15

Essentials of Modern Business Statistics (7 e) Mode Example: Monthly Starting Salary The only monthly starting salary that occurs more than once is $3, 880. Mode = 3, 880 Note: Data is in ascending order. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 16

Essentials of Modern Business Statistics (7 e) Excel’s Mean Median and Mode Functions Excel’s Mean Function q AVERAGE(data cell range) Excel’s Median Function q MEDIAN(data cell range) Excel’s Mode Function q MODE. SNGL(data cell range) © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 17

Essentials of Modern Business Statistics (7 e) Using Excel to Compute the Mean, Median, and Mode q Excel Formula Worksheet © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 18

Essentials of Modern Business Statistics (7 e) Using Excel to Compute the Mean, Median, and Mode q Excel Value Worksheet © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 19

Essentials of Modern Business Statistics (7 e) Weighted Mean § In some instances the mean is computed by giving each observation a weight that reflects its relative importance. § The choice of weights depends on the application. § The weights might be the number of credit hours earned for each grade, as in GPA. § In other weighted mean computations, quantities such as pounds, dollars, or volume are frequently used. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 20

Essentials of Modern Business Statistics (7 e) Weighted Mean § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 21

Essentials of Modern Business Statistics (7 e) Weighted Mean Example: Purchase of Raw Material Consider the following sample of five purchases of a raw material over a period of three months: Purchase Cost per Pound ($) Number of Pounds 1 3. 00 1200 2 3. 4 500 3 2. 8 2750 4 2. 9 1000 5 3. 25 800 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 22

Essentials of Modern Business Statistics (7 e) Weighted Mean § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 23

Essentials of Modern Business Statistics (7 e) Geometric Mean § The geometric mean is calculated by finding the nth root of the product of n values. § It is often used in analyzing growth rates in financial data (where using the arithmetic mean will provide misleading results). § It should be applied anytime you want to determine the mean rate of change over several successive periods (be it years, quarters, weeks, . . . ). § Other common applications include: changes in populations of species, crop yields, pollution levels, and birth and death rates. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 24

Essentials of Modern Business Statistics (7 e) Geometric Mean § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 25

Essentials of Modern Business Statistics (7 e) Geometric Mean Example: Mutual fund © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 26

Essentials of Modern Business Statistics (7 e) Geometric Mean § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 27

Essentials of Modern Business Statistics (7 e) Using Excel to Compute Geometric Mean q Excel Function for Geometric Mean = GEOMEAN(data cell range) © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 28

Essentials of Modern Business Statistics (7 e) Using Excel to Compute Geometric Mean q Excel Formula Worksheet © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 29

Essentials of Modern Business Statistics (7 e) Using Excel to Compute Geometric Mean q Excel Value Worksheet © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 30

Essentials of Modern Business Statistics (7 e) Percentiles § A percentile provides information about how the data are spread over the interval from the smallest value to the largest value. § Admission test scores for colleges and universities are frequently reported in terms of percentiles. § The pth percentile of a data set is a value such that at least p percent of the items take on this value or less and at least (100 - p) percent of the items take on this value or more. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 31

Essentials of Modern Business Statistics (7 e) Percentiles Arrange the data in ascending order. Compute Lp, the location of the pth percentile. Lp = (p/100)(n + 1) © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 32

Essentials of Modern Business Statistics (7 e) 80 th Percentile Example: Monthly Starting Salary Lp = (p/100)(n + 1) = (80/100)(12 + 1) = 10. 4 (the 10 th value plus. 4 times the difference between the 11 th and 10 th values) 80 th Percentile = 4050 + 0. 4 (4130 – 4050) = 4082 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 33

Essentials of Modern Business Statistics (7 e) 80 th Percentile Example: Monthly Starting Salary “At least 20% of the items take on a value of 4082 or more. ” 2/12 =. 167 or 16. 7% At least 80% of the items take on a value of 4082 or less. ” 10/12 =. 833 or 83% Monthly Starting Salary ($) 3, 710 3, 755 3, 850 3, 880 3, 890 3, 920 3, 940 3, 950 4, 050 4, 130 4, 325 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 34

Essentials of Modern Business Statistics (7 e) Using Excel to Compute Percentiles q Excel’s percentile function is: PERCENTILE. EXC(data range, p/100) © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 35

Essentials of Modern Business Statistics (7 e) Using Excel to Compute 80 th Percentile q Excel Formula worksheet 80 th Percentile Note: It is not necessary to put the data in ascending order. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 36

Essentials of Modern Business Statistics (7 e) Using Excel to Compute 80 th Percentile q Excel Value worksheet Note: It is not necessary to put the data in ascending order. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 37

Essentials of Modern Business Statistics (7 e) Quartiles are specific percentiles. q First Quartile = 25 th Percentile q Second Quartile = 50 th Percentile = Median q Third Quartile = 75 th Percentile © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 38

Essentials of Modern Business Statistics (7 e) Third Quartile (75 th Percentile) Example: Monthly Starting Salary Lp = (p/100)(n + 1) = (75/100)(12 + 1) = 9. 75 (the 9 th value plus. 75 times the difference between the 10 th and 9 th values) Third quartile = 3950 +. 75(4050 – 3950) = 4025 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 39

Essentials of Modern Business Statistics (7 e) Using Excel to compute Quartiles q Excel’s Quartile Function QUARTILE. EXC(array, QUART) © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 40

Essentials of Modern Business Statistics (7 e) Using Excel to compute 3 rd Quartile q Excel Formula worksheet 3 rd quartile Note: It is not necessary to put the data in ascending order. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 41

Essentials of Modern Business Statistics (7 e) Using Excel to Compute 3 rd Percentile q Excel Value worksheet Note: It is not necessary to put the data in ascending order. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 42

Essentials of Modern Business Statistics (7 e) Measures of Variability § It is often desirable to consider measures of variability (dispersion), as well as measures of location. § For example, in choosing supplier A or supplier B we might consider not only the average delivery time for each, but also the variability in delivery time for each. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 43

Essentials of Modern Business Statistics (7 e) Measures of Variability q q q Range Interquartile Range Variance Standard Deviation Coefficient of Variation © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 44

Essentials of Modern Business Statistics (7 e) Range § The range of a data set is the difference between the largest and smallest data values. Range = Largest value – Smallest value § It is the simplest measure of variability. § It is very sensitive to the smallest and largest data values. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 45

Essentials of Modern Business Statistics (7 e) Range Example: Monthly Starting Salary Range = largest value - smallest value Range = 4, 325 – 3, 710 = 615 Monthly Starting Salary ($) 3, 710 3, 755 3, 850 3, 880 3, 890 3, 920 3, 940 3, 950 4, 050 4, 130 4, 325 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 46

Essentials of Modern Business Statistics (7 e) Interquartile Range § The interquartile range of a data set is the difference between the third quartile and the first quartile. § It is the range for the middle 50% of the data. § It overcomes the sensitivity to extreme data values. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 47

Essentials of Modern Business Statistics (7 e) Interquartile Range (IQR) Example: Monthly Starting Salary § 3 rd Quartile (Q 3) = 4, 000 § 1 st Quartile (Q 1) = 3, 865 § IQR = Q 3 - Q 1 = 4, 000 – 3, 865 = 135 Monthly Starting Salary ($) 3, 710 3, 755 3, 850 3, 880 3, 890 3, 920 3, 940 3, 950 4, 050 4, 130 4, 325 © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 48

Essentials of Modern Business Statistics (7 e) Variance § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 49

Essentials of Modern Business Statistics (7 e) Variance § The variance is the average of the squared differences between each data value and the mean. § The variance is computed as follows: for a sample for a population © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 50

Essentials of Modern Business Statistics (7 e) Standard Deviation § The standard deviation of a data set is the positive square root of the variance. § It is measured in the same units as the data, making it more easily interpreted than the variance. © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 51

Essentials of Modern Business Statistics (7 e) Standard Deviation The standard deviation is computed as follows: For a sample For a population © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 52

Essentials of Modern Business Statistics (7 e) Excel’s Variance and Standard deviation Functions q Excel’s Sample Variance Function VAR. S(data cell range) q Excel’s Sample Standard deviation Function STDEV. S(data cell range) © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 53

Essentials of Modern Business Statistics (7 e) Coefficient of Variation § for a sample for a population © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 54

Essentials of Modern Business Statistics (7 e) Sample Variance, Standard Deviation, And Coefficient of Variation § © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 55

Essentials of Modern Business Statistics (7 e) Using Excel to compute the sample Variance, Standard Deviation and Coefficient of Variation q Excel Formula Worksheet © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 56

Essentials of Modern Business Statistics (7 e) Using Excel to compute the sample Variance, Standard Deviation and Coefficient of Variation q Excel Value Worksheet © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 57

Essentials of Modern Business Statistics (7 e) End of Chapter 3, Part A © 2018 Cengage Learning. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website or school-approved learning management system for classroom use. 58