Post on 31-Dec-2015
Forging new generations of engineers
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.