QMS 210 Problem Solving: Measures of Central Tendency & Variability

1 QMS 210 Problem Solving – Winter 2024 Session 2 1.Measures of central tendency Mode, Mean, Median 2.Measures of variability Range, Interquartile range, standard deviation and variance, Coefficient of variation 3. Which is a better measure of central tendency? Mean or Median? 4. Shape of Distribution – Skewness Problem 1. (Question 1 in MyLab) The following data reflect the number of defects produced on an assembly line at an electronics company for the past 7 days. 0 5 4 1 3 2 5 a. Compute the mean number of defects for this population of days. b. Compute the median number of defects produced for this population of days. c. Determine if there is a mode number of defects, and if so, indicate the mode value.

2 Problem 2. (Question 2 in MyLab) A hospital wants to compare its annual patient turnover rate per bed with similar hospitals. The turnover rates for a sample of 55 beds at the hospital are shown in the table below. Annual Turnover Rate Number of Beds 10 & under 15 6 15 & under 20 8 20 & under 25 11 25 & under 30 30 (An annual turnover of 21 per bed indicates that, during the year, 21 patients occupied the same hospital bed.) What is the mean turnover rate?

3 Problem 3. (Question 3 in MyLab) The following table is of profit, revenue, and number of employees of 4 companies. COMPANY TOTAL Revenue/employee No. of Profit US$ US $ Employees billion Exxon 11.9 96,180 122700 Royal Dutch 7.6 74,284 105100 British Petroleum 4.3 70,859 56470 Petrofina SA 2.2 67,392 69062 (a) For the 4 companies, find the mean profit per company (in billion US dollars). (b) Find the "overall" mean revenue per employee (i.e., for all employees of these firms combined) of the 4 companies (in US dollars). (c) What is the ``overall’’ mean profit per employee ($)?

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4 Problem 4. (Question 4 in MyLab) Using the following data, Chain # of Stores Avg. Sales/Store ($ 000) Toys 'R' Us 144 7,233 Child World 79 3,589 Kaybee 361 506 (1) find the average sales per chain (in $1000). (2) find the median sales per store ($). (3) find the overall average sales per store ($) (Round to the nearest integer).

5 Problem 5. (Question 5 in MyLab) The following sample data was obtained at 8:00 p.m. at a small restaurant. There were 5 tables occupied at the time. Number of Guests at Table Food Bill for Table in $ Liquor Bill for Table in $ 2 48.75 15.75 2 36.75 26.00 4 90.55 22.90 4 87.45 42.45 2 41.25 14.00 1) Find the mean food bill per table, and the standard deviation of the food bills at the 5 tables. 2) Find the mean liquor bill per table, and the standard deviation of the liquor bills at the 5 tables. 3) There was more relative variability in the food bill than the liquor bill?

6 Problem 6. (Question 8 in MyLab) The data set below shows the number of alcoholic drinks that students at a certain university reported they had consumed in the past month. 13 15 14 13 18 18 16 12 Find (1) the range, variance, standard deviation, and interquartile range assuming the data represents a sample; (2) the range, variance, standard deviation, and interquartile range assuming the data represents a population. The use of n − 1 instead of n in the formula for the sample variance is known as Bessel's correction , which corrects the bias in the estimation of the population variance, and some, but not all of the bias in the estimation of the population standard deviation. (source: https:/Unbiased_estimation_of_standard_deviation)

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7 Problem 7. (Question 23 in MyLab) The data set below contains spending on products ($) during a three-month period by a sample of 15 customers receiving incentives through a mobile loyalty program. 55.19 22.97 67.86 46.88 57.99 108.04 50.74 35.21 78.72 50.62 63.79 59.87 41.48 56.51 53.55 (a) Compute the mean and median. (b) Are the data skewed? If so, how?

8 Problem 8. (Question 9 in MyLab) The table below shows the number of one company's stores located in each of 50 regions. 65 97 25 28 75 30 53 42 563 35 81 160 65 41 17 342 11 138 307 5 128 204 22 55 30 70 200 230 130 24 66 69 56 22 77 85 82 406 34 40 95 20 115 145 159 115 84 40 47 100 a) Compute the mean, variance, and standard deviation for this population. b) What percentage of the 50 regions have stores within ±1, ±2, or ±3 standard deviations of the mean? c) Compare your findings in part (b) with what would be expected on the basis of the empirical rule. Are you surprised at the results in part (b)?

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QMS210Winter2024Session2

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