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Introduction to Statistics

Using Packages of Colored Candies

Statistics Lab

Purpose of Statistics:

Describe a set of numbers and then make accurate

inferences (a.k.a. educated guesses) about that group of

data based on incomplete information

Statistics Involves:

1) Gathering Data

2) Organizing Data (sometimes pictorially)

3) Analyzing Data

The Problems:

1)Although candies are sold by weight rather than volume, how many candies can I expect when I open a 1.69 oz package?

2) How likely is it that the numbers of colors in each package occurred randomly?

Gathering Data:

• Open your package of Candy

• Separate, count and record the number of each color in the package.

Organize the Data:

• Open an EXCEL Spreadsheet Document• Enter the Headings as shown

Organize the Data:

• Enter the data in the spreadsheet

Continue with the entire class’s information.

Analyzing Data: problem 1

Although candies are sold by weight rather than volume, how many candies can I expect

when I open a 1.69 oz package?

What do I need to know?

Analyzing Data:

Measures of Central Tendency

Mean

Median

Mode

= “Average”

= Number in the Middle

= Number used Most

Analyzing Data:

Measures of Variability

Range = Spread

Standard Deviation

= The “average” distance each piece of data is from the mean

Analyzing Data:

Insert the categories of Mean, Median, Range and Standard Deviation to your spreadsheet:

Analyzing Data:

Use the Insert > Function capabilities of Excel to do the calculations

Analyzing Data:

What do each of these calculations mean?

1) Supposed I only get 22 candies. Am I being cheated in “quantity”?

2) How about 74 candies?

Analyzing Data: problem 2

How can I test this?

How likely is it that the numbers of colors in each package occurred

randomly?

Analyzing Data: using an EXCEL function

ChiTest

A test for independence which returns the probability that your observed data

and your expected data are related.

In this case we are seeking an answer to: How likely is it that the candies counted

were packaged strictly by chance?

Analyzing Data:

Hypothesis:

The observed number of colored candies per package is not

significantly different than the number found if the candies were

packaged purely at random.

Analyzing Data:

The CHITEST returns a value between 0 and 1. The closer the number is to 1, the more likely your hypothesis is true.

Back to EXCEL

Analyzing Data:On your own: Mars company claims that their candies are packaged according to the following color percentages:

10% 10%

20%

30%

20%

10%

Use EXCEL CHITEST function to determine the probability that your bag of candies were packaged according to these

percentages.