Transcript Introduction to Statistics

Forging new generations of engineers
Introduction to Statistics
Statistics Lab
Using Packages of Colored Candies
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
= “Average”
Median
= Number in the Middle
Mode = Number used
Most
Analyzing Data:
Measures of Variability
Range = Spread
Standard = The “average”
Deviation
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 likely is it that the numbers of
colors in each package occurred
randomly?
How can I test this?
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%
30
%
20
%
20%
10
%
10
%
Use EXCEL CHITEST function to determine the probability
that your bag of candies were packaged according to these
percentages.