Topics for our first Seminar The readings are Chapters 1 and 2 of your textbook.

1. Topics for our first Seminar The readings are Chapters 1 and 2 of your textbook. Chapter 1 contains a lot of terminology with which you should be familiar. Chapter 2 contains instructions for creating and interpreting many statistical displays, graphs and charts. As Unit 2 begins tomorrow, we are going to discuss both Unit 1 and Unit 2 today. This will allow us to discuss the upcoming unit material before the week begins.

2. Categorizing Variables There are two types of variables: • Qualitative • Quantitative It is important to understand the difference between qualitative and quantitative variables –statistical techniques applied to them are different.

3. Definition: Qualitative Variables Itis an attribute –categorical data. Deals with type or quality. Examples: Names, Color, Size

4. Definition: Quantitative Variables Itis a measure or a count. Examples: Age, Weight, Speed There are two types of quantitative variables (two categories of quantitative variables) • Discrete • Continuous

5. Definition: Discrete Variables Discrete variables take on only certain values in an interval. The variable may be only an integer, for example. Example: The number of people in a room

6. Definition: Continuous Variable Continuous variables can take on any value within an interval. All values within a range are possible and are not limited. Example: Weight (can be a whole number or a decimal) Depth (can be a whole or decimal value, within a range of values)

7. Definition: Measurement Assigning a numerical value to a variable is a process called measurement. The measurement scale goes as follows: nominal, ordinal, interval, and ratio.

8. Definition: Nominal Data The nominal scale uses numbers for the purpose of identifying membership in a category. The items being measured have something in common. Example: Hair Color

9. Definition: Ordinal Data The ordinal scale places data in order -a greater than and less than measurement. Example: Contestants placing in a contest or race – first, second, third, etc. Salary Ranges in a company

10. Definition: Interval Data The interval scale has meaningful intervals between the numbers in the scale. (A difference of 20 is twice that of a difference of 10.) Example: Measuring feelings on a scale Temperature

11. Definition: Ratio Scale The ratio scale has the properties of the interval scale and in addition has a meaningful absolute zero. (Multiples are meaningful too.) Example: A person is twice as old as another person

12. Develop a Quantitative Analysis Model – Mathematical Model • Example (Pg 8) • Bill sells rebuilt springs for a price per units of $10. The fixed cost of the equipment to build the springs is $1,000. The variable cost per units is $5 for spring material. • Profit = Revenue – Expenses • Revenue is Selling Price per Unit (s) * Number of Units Sold (X) • Expenses is Fixed Cost (f) + Variable Cost • Variable Cost is Variable Cost per Unit (v) * Number of Units Sold (X) Profit = sX – f – vX • In this example: • s = 10 • f = 1,000 • v = 5

13. Math Model Example - Continued • Profit = sX – f – vX • Profit = $10X - $1,000 - $5X • If there are no sales, Bill will have a $1,000 loss. • If there are 1,000 units sold, Bill will have a profit of $4,000. • Break Even Point: • When the number of units sold results in $0 in profits. • 0 = sX – f – vX • Solving for x gives: • X = f / (s – v)

14. Frequency Distribution Terminology Class each category of the frequency distribution. Frequency is the number of data values falling in each class. Class Limits are the boundaries for each class. Class Interval is the width of each class. Class Mark is the midpoint of each class.

15. Histograms On page 57 in your textbook is a section titled “Creating a Frequency Distribution and Histogram” that illustrates the steps to create a histogram using Excel. Note a histogram is NOT the same thing as a bar chart. A histogram represents quantitative data (unlike a bar chart) and the bars in a histogram share one side (they touch).

16. Bar Charts On page 44 in your textbook is a section titled “Creating Charts in Excel 2007” that illustrates the steps to create a bar chart using Excel. Note a bar chart is NOT the same thing as a histogram. A bar chart represents qualitative data (unlike a histogram) and the sides of the bars in a bar chart have a gap between them.

17. Stem and Leaf Display A stem and leaf display is a variant of the frequency distribution. It consists of a stem (the leftmost numeral(s) of a number), a bar, and the leaves (the remaining numerals in The number. Example: if the data consisted of 28, 27, 32, 34, 36, 39 and 41, the stem would consist of the numerals 2, 3, and 4 and the leaves would be the numbers in the ‘ones’ place of the numbers. 2 8 7 3 2 4 6 9 4 1

18. Measures of Central Tendency Three common measures of center are: • (Arithmetic) Mean • Median • Mode Excel and the Data Analysis add-in can be used to calculate all three measures of center listed above.

19. Mean and Excel To use the following Statistical commands in Excel you need to open a blank Excel document first and click on a cell to make it active. Then, go to Insert on the Menu bar and then go to Function. Then, click on Statistical on the left side box. Example: If A1:A5 is named Scores and contains the numbers 10, 7, 9, 27, and 2, then to find the Average (Mean) value type the following in any empty cell: =AVERAGE(A1:A5) (don’t forget the “=” sign).

20. Measures of Spread (Dispersion) There are many common measures of spread: • Range • Deviation • Mean Absolute Deviation • Standard Deviation • Variance

21. Mean Absolute Deviation MAD (page 71) is the sum of absolute differences of all values from their mean divided by total number of data values. Example: Let's say you have values 3, 4, and 5. First, we need to find the mean: (3 + 4 + 5) / 3 = 12 / 3 = 4 MAD = [ | 3 - 4 | + | 4 - 4 | + | 5 - 4 | ] / 3 = [ | -1 | + | 0 | + | 1 | ] / 3 = (1 + 0 + 1) / 3 = 2/3 = 0.66667.

22. MAD and Excel You can also use Excel to calculate this for you. This is not in the book. Here is how to do it. Enter 3, 4, and 5 (remember that this is just a simple example and these numbers are chosen arbitrarily) into cells A1, A2, and A3. Now , click on an empty cell anywhere and then click on the Fx on the menu bar select "statistical" or “All” on the left side and then select AVEDEV (the top one) on the right side. Then click on OK. The result of MAD will be shown on the cell you chose. You will get the same answer: 0.666667

23. Standard Deviation and Excel To use the following Statistical commands in Excel you need to open a blank Excel document first and click on a cell to make it active. Then, go to Insert on the Menu bar and then go to Function. Then, click on Statistical on the left side box. Example: Suppose the sample values (1345, 1301, 1368, 1322, 1310, 1370, 1318, 1350, 1303, 1299) are stored in A1:A10, respectively. STDEV estimates the standard deviation of these numbers. So, =STDEV(A1:A10) equals 27.46.

24. Standard Deviation and Excel You can also use Descriptive Statistic option of Data Analysis. Simply open your dataset in an Excel worksheet, highlight it, go to “Tools” in Excel, then go to Data Analysis and select Descriptive Statistics. Then enter the range of your data (let's say you are doing it for our 3 numbers 3, 4, and 5 that are on A1, A2, and A3). So, here you enter A1:A3 in Input Range and click on "Summary Statistic" and Confidence Interval for Mean". Your descriptive statistics would open with lots of information in it. This is very useful. (These steps are also given on page 75, Computer Solutions 3.2)