iv. schedule datetopic (changes in chapters covered will be announced in class or on bb) th., 1/30...

IV. Schedule

Date Topic (Changes in chapters covered will be announced in class or on Bb)

Th., 1/30

Exam 1 (chapters 1, 2, and 3)

Th., 2/27

Exam 2 (chapters 6, 7, and 8)

Th., 4/3

Exam 3 (chapters 4, 13, 9, and 10)

Th., 4/24 (5:30-8:00)

Final Exam (comprehensive)

MAN 201

BUSINESS STATISTICS

Chapter 1Review Question

Review Question Chapter 1:

1. Why use a sample– Why not measure the entire population rather than rely on a sample?

2. When we use a sample to draw conclusion about the entire population what branch of business statistics are we talking about?

3. What are the two type of samples?

4. In systematic sampling every kth member of the population is chosen for the sample, How do you calculate the value k?

5. What type of sample is a internet poll?

Review Questions Chapter 1:

6. An inspector needs to examine a shipment to determine the extent of deterioration of the parts in the shipment. The shipment consists of 2,000 sealed cartons, each containing 5 parts. If a simple random sample of 100 parts is to be examined, it is conceivable that as many as 100 cartons may have to be unsealed. The inspector wishes to open fewer cartons. Their sampling procedure calls for the selection of 20 of the 2,000 cartons at random and inspection of all parts in each selected carton.

• What is the population size (N) ?• What is the entity?• What is the sample size?• What is the random sampling technique being used?


7. A state teachers’ association is studying the educational qualifications of its membership, which consist of 50,000 elementary school, high school, and college teachers. A major characteristic of interest is the mean number of years of education of its members. The analyst used a sample design in which independent simple random samples of teachers are selected from among the member teachers in each of the three school levels.

• What is the entity?• What is the sampling technique being used?


8. What are the two main data types?

9. What are the data types of the following variables?• Occupational status• Saving account balance• Number of classes a student has this semester

10. What the difference between a sample and a census?

MAN 201

BUSINESS STATISTICS

Chapter 2Organizing and Graphing Data

Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall

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• Recall the types of data from Chapter 1:

Displaying Quantitative Data

Quantitative Qualitative

Types of Data

Discrete Continuous Ordinal Nominal

Discrete vs. Continuous Data

• Discrete data are values based on observations that can be counted and are typically represented by whole numbers– represent something that has been counted– take on whole numbers such as 0, 1, 2, 3

• Continuous data are values that can take on any real numbers, including numbers that contain decimal points– usually measured rather than counted– Examples are weight, time, and distance

Nominal Scale vs. Ordinal Scale

• Nominal scale is one that simply lists names as potential categories. As an example, the variable type of industry produces nominal responses such as:– construction– banking– retail

• Ordinal scale involves a ranking or ordering of the categories. Various cuts of beef have such label as prime, choice, good, and so on, that imply difference in order.

• Usually qualitative data are measured on nominal or ordinal scales.

Organizing and Graphing Data

• The main purpose of this chapter is to present methods for organizing and displaying qualitative and quantitative data in tables and graphs.

• Result- we hope to achieve clarity and extract information that might not have been apparent about the sample in its raw, unprocessed form.

Constructing a Frequency Distribution

• A frequency distribution shows the number of data observations that fall into specific intervals

– Graphically summarize information not readily observable by merely looking at data in a table

Constructing a Frequency Distribution• Example: Number of iPads sold per day

Ungrouped frequency distribution: A table consisting of two columns of information • Values of the variable • Frequency with which each value occurs in the data set.

Relative Frequency Distributions

• Relative frequency distributions display the proportion of observations of each class relative to the total number of observations– shows the fraction of observations in each class – found by dividing each frequency by the total

number of observations– the fractions in a relative frequency distribution

add up to 1.00

Relative Frequency Distributions

Two iPads were sold on 28% of the days

Example:

Cumulative Relative Frequency Distributions

• A cumulative relative frequency distribution totals the proportion of observations that are less than or equal to the class at which you are looking– Shows the accumulated proportion as values vary

from low to high

• Example:

Three iPads or less were sold on 80% of the business daysPr(Number Sold Per Day <= 3) = 80%

Cumulative Relative Frequency Distributions

Using a Histogram to Graph a Frequency Distribution

• A histogram is a graph showing the number of observations in each class of a frequency distribution

The Shape of Histograms

• Symmetric– the right side is the mirror

image of the left side of the distribution

• Still symmetric, but wider spread

• Not symmetric

Grouped frequency distribution: A table consisting of two columns of information – the values of the variable organized into classes and the frequency of the values that occur within each class.

Constructing a Frequency Distribution Using Grouped Quantitative Data

• Ideally, the number of classes in a frequency distribution should be between 4 and 10– Some data sets, particularly those with continuous data,

require several values to be grouped together in a single class

– This grouping prevents having too many classes in the frequency distribution, which can make it difficult to detect patterns

Constructing a Frequency Distribution Using Grouped Quantitative Data

Example: 50 Dell Customer Support Hold Times (minutes)

Number of Classes

• One method to determine the number of classes in a frequency distribution is the rule

2k > nwhere k = Number of classes

n = Number of data points

• Find the lowest value of k that satisfies the rule

• Suppose n = 5025 = 32 < 50 (k = 5 is too small)26 = 64 > 50 (k = 6 is a good choice)

Class Width

• Once k is known, the width of each class can be found– The width is the range of numbers to put into each

class

k

value data Minimumvalue data Maximum widthclass Estimated

• There is no one correct answer for the class width.

• The goal is to create a histogram to clearly and usefully show the pattern in the data

• Often there is more than one acceptable way to accomplish this

Class Width

Class Width = (17.4 – 0.6) = 2.8 or 3 6

Class Boundaries

• Class boundaries represent the minimum and maximum values for each class– Choose class boundaries that are easy to read

0 to less than 3 minutes 3 to less than 6 minutes

6 to less than 9 minutes 9 to less than 12 minutes 12 to less than 15 minutes 15 to less than 18 minutes

Class Frequencies• Find class frequencies by counting and

recording the number of observations in each class – this is easier when the data are sorted

• Example:

Creating Group Frequency Distribution ReviewSolution:

– Sort the data in ascending order– Observe the size of your data set (n=?)– Determine the number of classes 2k > n– Find the class width

– Create the class boundaries based on your class width

– Tally the number of data points within each class to come up with your frequency distribution.

– Calculate relative frequency distribution and cumulative relative frequency distribution

k

MinMax widthclass

Rules for Classes for Grouped Data1. Equal-size classes. All classes in the frequency

distribution must be of equal width

2. Mutually exclusive classes. Class boundaries cannot overlap (Principle of Exclusion)

3. Include all data values. Make sure all data values are accounted for in the total row of the frequency distribution (Principle of Inclusion)

4. Avoid empty classes. It is undesirable for a histogram to display a class so narrow that there are no observations in it

5. Avoid open-ended classes (if possible). These violate the first rule of equal class sizes

• A stem and leaf display splits the data values into stems (the larger place values) and leaves (the smaller place value)

• By listing all of the leaves to the right of each stem, we can graphically describe how the data are distributed– All the original data points are visible on the display– Easy to construct by hand– Provides a histogram-like view of the distribution

Stem and Leaf Display


1. Sort the data from lowest to highest2. Determine the unique stem values

7, 8, 9 are the different stem values in this example

3. List the stems in a vertical column and then add the leaf values to the right of the appropriate stem, in ascending order

7 | 8 8 9 9 9

8 | 0 0 0 0 1 1 2 3 3 4 4 4 5 6 7 89 | 0 2 5


• To get more detail the stems can be split in half

7(5) | 8 8 9 9 98(0) | 0 0 0 0 1 1 2 3 3 4 4 48(5) | 5 6 7 89(0) | 0 29(5) | 5

– The stem labeled 7(5) stores all the scores between 75 and 79– The stem 8(0) stores all the scores between 80 and 84

Pie Charts• Pie charts are another excellent tool for

comparing proportions for categorical data• Each segment of the pie represents the

relative frequency of one category– All categories in the data set must be included in

the pie

– Use a pie chart to compare the relative sizes of all possible categories


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Chapter 2 Homework Assignment


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70.5 - 76.5 76.5 - 82.5 82.5 - 88.5 88.5 - 94.5 94.5 - 100.50.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.200

0.267

0.367

0.133

0.033

Computer Homework Assignment #1

MGMT 201 Computer Homework #1

Note: Computer homework assignments are individual assignments and must be done

without assistance from or collaboration with other members of the class. Collaboration on Computer Homework assignments will result in zero credit for the assignment.

The purpose of this assignment is to help you get started using Excel to perform some of the basic statistical functions we’ve talked about in class. The data set is 100 responses to a survey given last year to MGMT 201 students. The questions in the survey are shown below:

1. Your age converted to months (e.g., 20 years and 3 months would be 243 months):

2. Distance in miles from where you lived during high school to UofL:

3. Your GPA:

4. Your major or planned major:

5. Your class year at UofL (F=freshman, S=sophomore, J=junior, R=senior, G=grad, O=other):

6. Have you taken statistics previously, either in high school or college? (yes or no)

7. Your level of anxiety about this course on a 1-5 scale with 1 = none and 5 = very high:

8. Average number of hours per week you work (for pay):

9. Number of other classes currently enrolled in: Indicate number (indicate 0, 1, 2 etc.)

10. The average number of hours per week you study during a normal semester.

The spreadsheet with the survey results is posted on Blackboard for this assignment. The data values for the 100 students are arranged in columns in the spreadsheet. The requirements of this assignment are shown below. We will use this data set for at least one other computer homework assignment.

1. The first thing you will have to do create descriptive statistics for the all quantitative variables.

a. To do this, click on the Data tab at the top of the spreadsheet. The far right section of the menu bar should be labeled “Analysis” and should include an item titled “Data Analysis.” If Data Analysis does not appear, click on the File tab at the far left of the tab bar, then click on Options (near the bottom), then click on Add-Ins (next to the bottom of the list at the left of the window), then look at the bottom of the window and you’ll see “Manage:” next to a drop down box. Make sure “Excel Add-ins” appears in the box, then click “Go.” In the Add-Ins window that appears, check “Analysis ToolPak,” then click “OK.” Then restart Excel and “Data Analysis” should appear in the Data toolbar.

To create descriptive statistics for the responses to each quantitative question, Click on “Data Analysis” then click on “Descriptive Statistics.” Put the range of the responses you want descriptive statistics for in the “Input Range” filed, click on “Grouped By” Columns, check the “Labels in First Row” box, select “Output Range” and insert a cell address that you want to be the upper left corner of the output range, check the “Summary statistics” box and click “OK.” Make sure you include

a. the variable in your Input Range. b. Make sure the count is 100 for all the quantitative variables.

2. Frequency distributions:

a. Have Excel create grouped frequency distribution for the Age(Months) distance variables. Make sure the frequency distributions include frequency, relative frequency and cumulative relative frequency.

b. Create Histograms for the Age(Months and distance variables. Briefly describe the shapes of the histograms.

c. Create ungrouped frequency distributions for the qualitative variables -- “Major,” the “Class Year” and the “Stat Class ?”. For the Class Year data, you should have five values of the variable (Freshman,Sophmore, Junior, Senior, Graduate) and for the Major data you should have 11 values and for the “Stat Class?” question you will have two values. Make sure the frequency distributions include frequency, relative frequency and cumulative relative frequency.

d. Create Histograms for Class Year, Major, and Stat Class variables. Briefly describe the shape of the histogram.

3. Pie Chart a. Recode the anxiety variables to 1 = none 2= very low 3=low, 4= high and 5 = very

high b. Create pie chart on the recoded values. Briefly describe the results of the pie

chart. Deliverable

One-page Excel spreadsheet with descriptive statistics for all of the quantitative variables,

One-page Excel spreadsheet with the frequency distributions, histogram and description for the Age, and distance variables.

One-page Excel spreadsheet with the frequency distributions, histogram and description for the qualitative variables -- “Major,” the “Class Year” and the “Stat Class ?” variables.

One-page Excel pie chart and description for the anxiety variable. The page must be landscape oriented (one point) with your name on top.

Everything must be typed – any hand-written numbers, notes, corrections or explanations will be ignored.

Due Thursday, Jan 23th at the beginning of class.

EXCEL Tutorial and Examples

Statistical Analysis Using Excel 20101. With Excel 2010 open,

click on the File tab found in the upper left corner of your computer screen

2. Click Options shown in the drop down menu. This will open the Excel Options dialog box

3. Select Add-Ins in the left margin…

4. Click on Go at the bottom of the screen

5. Select the check boxes for Analysis ToolPak and Analysis ToolPak - VBA in the popup menu and click OK

Statistical Analysis Using Excel 2010

Statistical Analysis Using Excel 2010

6. Select the Data tab. Click on Data Analysis on the right side of the application bar

The Data Analysis pop-up menu should appear in the spreadsheet

Constructing a Histogram in Excel1. Select the Data

tab, and click on Data Analysis in the upper right corner

2. In the pop-up menu, select Histogram and click OK…


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Constructing a Histogram in Excel3. In the Input Range

text box, highlight the desired data

4. In the Bin Range text box, highlight the bin values (create bins if not already created before step 1)

5. For Output options, select New Worksheet Ply and Chart Output

6. Click OK


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• Additional formatting issues:– Use a descriptive title for the graph– Use descriptive labels for the axes– Remove the redundant “Frequency” legend– Remove gaps between bars

Constructing a Histogram with Grouped Quantitative Data

The Consequences of Too Few or Too Many Classes

• Wide classes results in few class intervals

– Can obscure important patterns – Gives a “blocky” distribution graph– Summarizes the data too much– Tells us little about the true distribution shape

• Too many narrow classes in a histogram also has consequences

– Results in a “jagged” histogram– Some classes may be empty– Does not summarize the data enough


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• Qualitative data are values that are categorical– Can be nominal or ordinal measurement level– Describe a characteristic, such as gender or level of

education

• Frequency distributions help display qualitative data by indicating the number of occurrences of various categories– Can use Excel’s COUNTIF function to count the

number of values matching a category label

Displaying Qualitative Data

Displaying Qualitative Data


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Excel’s COUNTIF Function

Bar Charts• Bar charts are a good

tool for displaying qualitative data that have been organized in categories

• Can be arranged in a vertical or horizontal orientation


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Bar Charts Horizontal bar chart Vertical bar chart


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Can display multiple series with clustered bar charts or stacked bar charts:

Pie Charts


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Constructing a Pie Chart in Excel

Pie Charts


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Constructing a Pie Chart in Excel(continued)


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Class Assignment:

• Read chapter 3 pages 91-115, 120-126, and 131-141

• Work problems: 3.6, 3.8, 3.11,3.20, 3.35, 3.40, 3.50, 3.64, 3.66, 3.68.

iv. schedule datetopic (changes in chapters covered will be announced in class or on bb) th., 1/30...

Documents

graphing data slide

continuous data discrete

distance slide

sample size

review questions chapter

sample design

main data types

review question chapter