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 shouldbe familiar.

Chapter 2 contains instructions for creating and interpretingmany 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.

Categorizing Variables

There are two types of variables:• Qualitative• Quantitative

It is important to understand the difference betweenqualitative and quantitative variables –statistical techniquesapplied to them are different.

Definition: Qualitative Variables

It is an attribute –categorical data.Deals with type or quality.

Examples:Names, Color, Size

Definition: Quantitative Variables

It is a measure or a count.

Examples:Age, Weight, Speed

There are two types of quantitative variables (two categoriesof quantitative variables)• Discrete• Continuous

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

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)

Definition: Measurement

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

Definition: Nominal Data

The nominal scale uses numbers for the purpose of identifyingmembership in a category. The items being measured have something in common. Example:Hair Color

Definition: Ordinal Data

The ordinal scale places data in order -a greater than and lessthan measurement. Example:Contestants placing in a contest or race – first, second, third,

etc.

Salary Ranges in a company

Definition: Interval Data

The interval scale has meaningful intervals between thenumbers in the scale. (A difference of 20 is twice that of adifference of 10.) Example:Measuring feelings on a scale

Temperature

Definition: Ratio Scale

The ratio scale has the properties of the interval scale and inaddition has a meaningful absolute zero. (Multiples aremeaningful too.) Example:A person is twice as old as another person

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

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)

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.

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).

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 betweenthem.

Stem and Leaf Display

A stem and leaf display is a variant of the frequencydistribution. It consists of a stem (the leftmost numeral(s) ofa number), a bar, and the leaves (the remaining numerals inThe number.

Example: if the data consisted of 28, 27, 32, 34, 36, 39 and41, the stem would consist of the numerals 2, 3, and 4 andthe leaves would be the numbers in the ‘ones’ place of thenumbers.

2 8 7 3 2 4 6 94 1

 

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 allthree measures of center listed above.

Mean and Excel

To use the following Statistical commands in Excel you needto open a blank Excel document first and click on a cell tomake it active. Then, go to Insert on the Menu bar and thengo to Function. Then, click on Statistical on the left sidebox.

Example: If A1:A5 is named Scores and contains thenumbers 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).

Measures of Spread (Dispersion)

There are many common measures of spread:• Range• Deviation• Mean Absolute Deviation• Standard Deviation• Variance

Mean Absolute Deviation

MAD (page 71) is the sum of absolute differences of all valuesfrom their mean divided by total number of data values.

Example: Let's say you have values 3, 4, and 5. First, weneed 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.

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 exampleand these numbers are chosen arbitrarily) into cells A1, A2,and A3. Now , click on an empty cell anywhere and then clickon the Fx on the menu bar select "statistical" or “All” on theleft side and then select AVEDEV (the top one) on the rightside. Then click on OK. The result of MAD will be shown on thecell you chose.

You will get the same answer: 0.666667 

Standard Deviation and Excel

To use the following Statistical commands in Excel you needto open a blank Excel document first and click on a cell tomake it active. Then, go to Insert on the Menu bar and thengo to Function. Then, click on Statistical on the left sidebox.

Example: Suppose the sample values (1345, 1301, 1368,1322, 1310, 1370, 1318, 1350, 1303, 1299) are stored inA1:A10, respectively.

STDEV estimates the standard deviation of these numbers.So, =STDEV(A1:A10) equals 27.46.

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 selectDescriptive Statistics. Then enter the range of your data (let'ssay you are doing it for our 3 numbers 3, 4, and 5 that are onA1, A2, and A3). So, here you enter A1:A3 in Input Rangeand click on "Summary Statistic" and Confidence Interval forMean". Your descriptive statistics would open with lots ofinformation in it. This is very useful. (These steps are alsogiven on page 75, Computer Solutions 3.2)