Textbook Notes (368,566)
Canada (161,966)
QMS 230 (8)
Chapter 3

Chapter 3 Worksheet

20 Pages
153 Views
Unlock Document

Department
Quantitative Methods
Course
QMS 230
Professor
Douglas Mc Kessock
Semester
Fall

Description
CQMS204- Statistics for Management Chapter#3 Chapter3 Numerical Descriptive Measures Measures of Central Tendency (use calc) Outcomes: 1. Differentiate between the mean, the median, and the mode of data 2. State the advantages and disadvantages of the three measures Central Values 1. The mean, the mode and the median are referred to as measures of central tendency. 2. These three measures are indicators of typical middle values in the data set. 3. The mean is the arithmetic average of all values in the data set. 1 answer 4. The median indicates the halfway point. 5. The mode is the most frequently occurring value. Multiple answers The Mean a. The Arithmetic Mean when all values = the same weight sample mean x x = n population mean = x N b. The Weighted Mean when values are weighted different (ex. Marks) wx x = w where x = the sample mean; = the population mean; x = the observed values; n = the number of observations in the sample; N =the number of observations in the population; w = weights, i.e numbers to indicate the relative importance of each data value in the overall result; wx = the weighted values of the observed values; wx = the sum of the weighted values Note: the symol read sigma and denotes the summation of values. Winter2011 Page1 CQMS204- Statistics for Management Chapter#3 c. The population mean of Grouped Data fm = f where = the mean of the data set; m = the individual class midpoints; midpoint = lower + upper / 2 f = the number of observations in each class; f = the total number of observations in the data set; fm = the sum of the weighted values of the class midpoints The Median The median of Ungrouped Data Position number of median in an array =+ 1 2 The Mode the most frequently occurring value Example1 The annual incomes of a sample of middle-management employees at Ryerson Inc. are: $45,000, $50,000, $55,000, $50,000, $53,000, $47,000 a. Determine the sample mean, mode and median. b. Is the mean we determined in (a) a statistic or a parameter? Why? a) Mean (or x bar): 50,000 Mode: 50,000 Median: 50,000 b) Statistics. Because we are calculating for a sample. Example2 There are 11 salespeople employed by Midtown Inc. The numbers of new cars sold last month by the respective salespeople were: 15, 23, 28, 9, 19, 18, 10, 10, 8, 28, 19 a. Determine the population mean, mode and median. b. Is the mean we determined in (a) a statistic or a parameter? Why? a) Mean (or mew (because its population): 17 Mode: 10, 19 & 28 Median: 18 b) Parameter. Because it is a population. Winter2011 Page2 CQMS204- Statistics for Management Chapter#3 10% rule: 1. Calculate the difference between the mean and median 2. Calculate 10% of the smaller of the mean or m~dian 3. If the difference <10% of smaller conclude x = x in which case the mean is the preferred measure. 4. If the difference >10% of smaller conclude x x in which case the median is the preferred measure. Example3 a. The following data represents the prices of houses sold last week in a particular neighbourhood. $200,000 $205,000 $210,000 $220,000 $225,000 What is the appropriate measure of central tendency for these data? Why? 1. Mean (x bar): 212000 Median (x with squiggly on top): 210000 Mean Median = 212,000 210,000 = 2,000 2. 210,000 (cause its smaller) * 0.1 = 21,000 3. Since 2,000 < 21,000, therefore you can use Mean or Median. (refer to 3 for 10% rule). However mean is better! So use mean. b. The following data represents the prices of houses sold last week in a particular neighbourhood. $200,000 $205,000 $210,000 $220,000 $425,000 What is the appropriate measure of central tendency for these data? Why? 1. Mean (x bar): 252,000 Median (x with squiggly on top): 210,000 Mean Median = 252,000 210,000 = 42,000 2. 210,000 * 0.1 = 21,000 3. 42,000 > 21,000, therefore it is Median. (refer to 4 for 10% rule) Example4 A&A Marketing Research Company is studying the number of times the ATM located in G&G Grocery Store at Yong and Finch is used per day. Following are the numbers of times the machine was used over each of the last 30 days. 82, 79, 84, 78, 82, 82, 77, 83, 88, 85, 84, 77, 79, 78, 79, 75, 78, 82, 82, 83, 82, 74, 78, 78, 78, 82, 78, 83, 85, 83. a. Determine the sample mean, mode and median. b. Is the mean we determined in (a) a statistic or a parameter? Why? Winter2011 Page3 CQMS204- Statistics for Management Chapter#3 a) Mean (x bar = sample): 80.6 Mode: 78, 82 Median: 82 b) Statistic because we are using sample. Example5 The Bookstall Inc. is a specialty bookstore concentrating on used books sold via the internet. Paperbacks are sold at $1.00 each, and hardcover books are $4.50. Of the 60 books sold last Thursday morning, 48 were paperback and the rest were hardcover. What was the weighted mean price of a book? X W (frequency) 1 48 4.50 12 Weighted Mean (x bar) = $1.7 Example6 There is intense competition among the long distance phone business. In an effort to study the actual phone usage of residential customers, an independent agency gathered the following sample information on the number of phone calls per household for the last week. Number of phone calls 2 3 4 5 6 7 (X) Number of 15 11 21 12 23 18 households(W) Determine the sample mean, mode and median. X W(frequency) 2 15 3 11 4 21 5 12 6 23 7 18 Mean (x bar): 4.71 Mode: 6 (because it occurs the most) Median: 5 Example7 Winter2011 Page4
More Less

Related notes for QMS 230

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit