Learning Objectives

Learning Objectives In this chapter, you will learn: • How statistics is used in business • The sources of data used in business • The types of data used in business • The basics of Microsoft Excel

Why Study Statistics? Decision Makers Use Statistics To: • Present and describe business data and information properly • Draw conclusions about large populations, using information collected from samples • Make reliable forecasts about a business activity • Improve business processes

Types of Statistics • Statistics • The branch of mathematics that transforms data into useful information for decision makers. Descriptive Statistics Collecting, summarizing, and describing data Inferential Statistics Drawing conclusions and/or making decisions concerning a population based only on sample data

Statistics • Specific number numerical measurement determined by a set of data Example: Twenty-three percent of people polled believed that there are too many polls.

Descriptive Statistics • Collect data • ex. Survey • Present data • ex. Tables and graphs • Characterize data • ex. Sample mean =

Inferential Statistics • Estimation • ex. Estimate the population mean weight using the sample mean weight • Hypothesis testing • ex. Test the claim that the population mean weight is 120 pounds Drawing conclusions and/or making decisions concerning a population based on sample results.

Statistics • Method of analysis a collection of methods for planning experiments, obtaining data, and then then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data

Basic Vocabulary of Statistics

Population vs. Sample Population Sample Measures used to describe the population are called parameters Measures computed from sample data are called statistics

Why Collect Data? • A marketing research analyst needs to assess the effectiveness of a new television advertisement. • A pharmaceutical manufacturer needs to determine whether a new drug is more effective than those currently in use. • An operations manager wants to monitor a manufacturing process to find out whether the quality of product being manufactured is conforming to company standards. • An auditor wants to review the financial transactions of a company in order to determine whether the company is in compliance with generally accepted accounting principles.

Sources of Data • Primary Sources: The data collector is the one using the data for analysis • Data from a political survey • Data collected from an experiment • Observed data • Secondary Sources: The person performing data analysis is not the data collector • Analyzing census data • Examining data from print journals or data published on the internet.

Types of Variables • Categorical (qualitative) variables have values that can only be placed into categories, such as “yes” and “no.” • Numerical (quantitative) variables have values that represent quantities.

Types of Variables • Examples: • Marital Status • Political Party • Eye Color • (Defined categories) • Examples: • Number of Children • Defects per hour • (Counted items) • Examples: • Weight • Voltage • (Measured characteristics)

Levels of Measurement • A nominal scale classifies data into distinct categories in which no ranking is implied. Categorical Variables Categories Personal Computer Ownership Type of Stocks Owned Internet Provider Yes / No Growth Value Other Microsoft Network / AOL

Levels of Measurement • An ordinal scale classifies data into distinct categories in which ranking is implied Categorical Variable Ordered Categories

Levels of Measurement • An interval scale is an ordered scale in which the difference between measurements is a meaningful quantity but the measurements do not have a true zero point. • A ratio scale is an ordered scale in which the difference between the measurements is a meaningful quantity and the measurements have a true zero point.

Interval and Ratio Scales

Discrete data result when the number of possible values is either a finite number or a ‘countable’ number of possible values 0, 1, 2, 3, . . . • Continuous (numerical) data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps 2 3

Discrete The number of eggs that hens lay; for example, 3 eggs a day.

Definitions • Discrete The number of eggs that hens lay; for example, 3 eggs a day. • Continuous The amounts of milk that cows produce; for example, 2.343115 gallons a day.

Microsoft Excel Terms • When you use Microsoft Excel, you place the data you have collected in worksheets. • The intersections of the columns and rows of worksheets form boxes called cells. • If you want to refer to a group of cells that forms a contiguous rectangular area, you can use a cell range. • Worksheets exist inside a workbook, a collection of worksheets and other types of sheets, including chart sheets that help visualize data.

Designing Effective Worksheets • You should associate column cell ranges with variables. • You do not skip any rows as you enter data, so column cell ranges will never contain any empty cells. • Place all the variables on a worksheet that is separate from the worksheet containing the statistical results. • Allow the user to be able to explicitly see the chain of calculations from the starting data. • Create two copies of your worksheets: one optimized for the screen, the other for the printer.

Stem Leaves Stem-and Leaf Plot Raw Data (Test Grades) 67 72 85 75 89 89 88 90 99 100 6 7 8 9 10 7 2 5 5 8 9 9 0 9 0

Example: Create a Stem and Leaf Plot for the following data which represents ages of CEO's: 53 45 41 36 55 50 37 48 52 62 43 46 39 50 52 61 48 37 48 55 59 52 39 41 50 The TI-83 will not create the Stem and Leaf Plot for you completely, but it will allow you to sort the data which makes creating the chart by hand easy. Here is what to do:

Enter the data into a free list (use L1 if it is available). Recall that you do this by hitting STAT, then 1 for Edit and clear L1 if necessary. After you have entered the data into L1 the screen should look like this:

2. Now hit 2nd MODE for quit to get to the homescreen. Now hit STAT to get this screen: 3. Now select 2 to get SortA(which stands for Sort Ascending). Your screen will look like this:

4. Enter the list you wish to sort in this case L1 (hit 2nd 1). Your screen looks like this 5. Now hit enter, the screen will say done. Hit Stat then edit to get back to the editor. Your data should be sorted. Here is what the screen should look like:

Stem Leaf 3 3 67799 4 1135 4 6888 5 00222355 5 9 6 12

Definitions • Median • the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

Definitions • Median • the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude • often denoted by x (pronounced ‘x-tilde’) ~

Definitions • Median • the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude • often denoted by x (pronounced ‘x-tilde’) • is not affected by an extreme value ~

6.72 3.46 3.60 6.44 3.46 3.60 6.44 6.72 no exact middle -- shared by two numbers (even number of values) 3.60 + 6.44 MEDIAN is 5.02 2

6.72 3.46 3.60 6.44 26.70 3.46 3.60 6.44 6.72 26.70 (in order - odd number of values) exact middle MEDIANis 6.44 6.72 3.46 3.60 6.44 3.46 3.60 6.44 6.72 no exact middle -- shared by two numbers (even number of values) 3.60 + 6.44 MEDIAN is 5.02 2

Qualitative vs Quantitative • Number of students who turn a paper in late. • Sex of the next baby born in a hospital. • Amount of fluid in a machine to fill bottles of soda pop. • Brand of a personal computer. • Zip Codes.

Discrete vs Continuous • Price of a textbook. • The length of a new born baby. • The number of bad checks received by a store. • Concentration of a contaminant in a solution. • Actual weight of a 1-lb can of coffee.

Measures of Position Quartiles, Deciles, Percentiles

Quartiles Q1, Q2, Q3

Quartiles Q1, Q2, Q3 divides ranked scores into four equal parts 25% 25% 25% 25% Q1 Q2 Q3

Deciles D1, D2, D3, D4, D5, D6, D7, D8, D9 divides ranked data into ten equal parts

10% 10% 10% 10% 10% 10% 10% 10% 10% 10% D1 D2 D3 D4 D5 D6 D7 D8 D9 Deciles D1, D2, D3, D4, D5, D6, D7, D8, D9 divides ranked data into ten equal parts

Quartiles Q1 = P25 Q2 = P50 Q3 = P75

Range The difference between the highest and lowest score • Interquartile Range (or IQR): Q3 - Q1

Interquartile Range (or IQR): Q3 - Q1 • Semi-interquartile Range: (Q3- Q1)/2 • Midquartile: (Q1+ Q3)/2 • 10 - 90 Percentile Range: P90 - P10 • Midrange: (smallest + largest)/2

Finding the Percentile of a Given Score number of scores less than x Percentile of score x = • 100 total number of scores

k R = • n 100 Finding the Score Given a Percentile n total number of values in the data set kpercentile being used R locator that gives the position of a value Pkkth percentile

) k ( 100 Start Finding the Value of the kth Percentile Sort the data. (Arrange the data in order of lowest to highest.) Compute L = nwhere n = number of values k = percentile in question The value of the kth percentile is midway between the Lth value and the next value in the sorted set of data. Find Pk by adding the L th value and the next value and dividing the total by 2. Is L a whole number ? Yes No Change L by rounding it up to the next larger whole number. The value of Pk is the Lth value, counting from the lowest

Stem Leaves 6 7 8 9 10 7 2 5 5 8 9 9 0 9 0 Stem-and Leaf Plot Raw Data (Test Grades) 67 72 85 75 89 89 88 90 99 100 Find P33 Find P50 P50= P33= P50= the mean of the 5th and 6th score or 88.5 P33= round up to 4, the fourth score is 85

Stem Leaves 6 9 2 3 4 5 6 7 8 8 9 0 1 1 4 1 2 3 Stem-and Leaf Plot Raw Data 16 19 22 23 24 25 26 27 28 28 29 30 31 31 34 Find P30 Find P50 P50= P30= P50= round up to 8, the eight score is 27 P30= round up to 5, the fifth score is 24

Stem Leaves 6 9 2 3 4 5 6 7 8 8 9 0 1 1 4 1 2 3 Stem-and Leaf Plot Raw Data 16 19 22 23 24 25 26 27 28 28 29 30 31 31 34 What percentile is 22? What percentile is 30? 11/15 = 73rd percentile 2/15 = 13th percentile

Learning Objectives