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SBE10 CP03 - Chapter 3 Descriptive Statistics Numerical...

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Chapter 3 Descriptive Statistics: Numerical Methods Chapter 3 Descriptive Statistics: Numerical Methods Case Problem 1: Pelican Stores 1. Descriptive statistics for all customers are shown followed by the same descriptive statistics for 4 subgroups of customers. Net Sales (All Customers) Mean $77.60 Median $59.71 Std. Dev. $55.66 Range $274.36 Skewness 1.715 NET SALES BY CUSTOMER TYPE Married Single Regular Promotion Mean $78.03 $77.04 $61.99 $85.25 Median 59.00 69.00 51.00 63.64 Std. Deviation 57.67 46.21 35.07 61.38 Range 274.36 163.30 137.25 274.36 Skewness 1.732 1.254 1.351 1.520 A few observations can be made: a. Customers taking advantage of the promotional coupons spent more money on average. The mean amount spent by all customers is $77.60; the average amount spent by promotional customers was $85.25. b. The standard deviation of sales is $55.66. This indicates a fairly wide variability in purchase amounts across customers. This variability is quite a bit smaller for the regular customers. c. The distribution of the sales data is skewed to the right. The mean ($77.60) is larger than the median ($59.71) and the skewness measure (1.715) is positive. Positive skewness is typical for this kind of data. There are no negative sales amounts and there are a few large purchases. There are many other descriptive statistics students may generate using the other variables. These will lead to other observations concerning the demographics of the Pelican customers and their buying behavior. For example, the following crosstabulation shows data for the 70 female customers classified by type of customer and marital status. CP - 9
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Chapter 3 Descriptive Statistics: Numerical Methods Gender Marital Status Female Female Total Grand Total Type of Customer Data Married Single Promotional Average of Age 44 33 43 43 Average of Net Sales 86.48 75.96 85.20 85.20 Count of Customer 58 8 66 66 Regular Average of Age 44 42 44 44 Average of Net Sales 58.81 89.50 64.49 64.49 Count of Customer 22 5 27 27 Total Average of Age 44 36 43 43 Total Average of Net Sales 79 81 79 79 Total Count of Customer 80 13 93 93 We see that for the 58 female-married promotional customers the average net sales was $86.48, and that for the 8 female-single promotional customers the average net sales was $75.96. Thus, for the promotional customers the average net sales are greater for the married female customers. Note, however, that this effect is just the opposite for the regular customers. For the female-married promotional customers the average net sales is also much greater than the average net sales for the female-married regular customers. 2. The correlation coefficient for the association of sales with age is r = .01. There does not appear to be any relationship between net sales and age. Case Problem 2: The Motion Picture Industry This case provides the student with the opportunity to use numerical measures to continue the analysis of the motion picture industry data first presented in Chapter 2. Developing and interpreting descriptive statistics such as the mean, median, standard deviation and range are emphasized. Five-number summaries
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