Describing Data Using Statistics Statistics and Risk Management Copyright © Texas Education Agency,...

Copyright © Texas Education Agency, 2012. All rights reserved. 1

Describing Data Using Statistics

Statistics and Risk Management


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Tools of Knowledge

Statistics:

The study of collecting, organizing, and analyzing data.• For Research• For Reporting


When Did This Come About?

We find Statistical Information (State of Things) in 1749. By the 18th century, the term "statistics" designated the

systematic collection of demographic and economic data by states.

In the early 19th century, the meaning of "statistics" broadened, then including the discipline concerned with the collection, summary, and analysis of data.


Vocabulary to Know

• Population: is the over all group of subjects to which the research will apply.

• Sample: is a smaller, more practical, group size that represents the larger population.

Subjects:


Research Statistics?

• Descriptive Statistics: Procedures used to organize and present data in a convenient and communicable form.

• Inferential Statistics: Procedures employed arrive at broader conclusions or inferences about populations on the basis of samples.


Data Types

Qualitative Data Quantitative Data

Discrete data Continuous data


Sample Measurements

• Count: Total Number of Scores in a set• Low/High: The Extreme Values-lowest and

highest in a set• Range: From the Low to the High-the distance

between the lowest and the highest. For example if my lowest number in the set was 2 and my highest number in the set was 20, my range would be 18.

20-2 = 18

The Count = 24

• 9:00 pm210

• 9:00 am205

• 1:00 pm200

• 6:00 pm180

• 10:00 am 170• 12:00 am 170• 2:00 pm

170• 10:00 pm 161• 8:00 am 160• 3:00 pm

152• 11:00 am 150• 8:00 pm 143

• 4:00 pm 140• 5:00 pm 130• 6:00 am 120• 7:00 am 110• 7:00 pm 100• 11:00 pm 80• 12:00 am 40• 2:00 am 40• 1:00 am 30• 3:00 am 20• 4:00 am 10• 5:00 am 31

The High = 210

• 9:00 pm210

• 9:00 am205

• 1:00 pm200

• 6:00 pm180

• 10:00 am 170• 12:00 am 170• 2:00 pm

170• 10:00 pm 161• 8:00 am 160• 3:00 pm

152• 11:00 am 150• 8:00 pm 143


The Low = 31

• 9:00 pm210

• 9:00 am205

• 1:00 pm200

• 6:00 pm180

• 10:00 am 170• 12:00 am 170• 2:00 pm

170• 10:00 pm 161• 8:00 am 160• 3:00 pm

152• 11:00 am 150• 8:00 pm 143


The Range = 179• 9:00 pm

210• 9:00 am

205• 1:00 pm

200• 6:00 pm

180• 10:00 am 170• 12:00 am 170• 2:00 pm

170• 10:00 pm 161• 8:00 am 160• 3:00 pm

152• 11:00 am 150• 8:00 pm 143


What about a sample with an odd number of scores? Copyright © Texas Education Agency, 2012. All rights reserved.


Measures of Central Tendencies

• Mode: The most repeated score• Median: The score(s) in the middle• Mean: The average of all scores

Let’s take a look at a more descriptive reference of these three measures of central tendencies…http://faculty.washington.edu/chudler/statistics.html

http://faculty.washington.edu/chudler/statistics.html

http://faculty.washington.edu/chudler/statistics.html

The Median: (143+140)/2=141.5• 9:00 pm 210• 9:00 am 205• 1:00 pm 200• 6:00 pm 180• 10:00 am 170• 12:00 am 170• 2:00 pm 170• 10:00 pm 161• 8:00 am 160• 3:00 pm 152• 11:00 am 150• 8:00 pm 143


What about a sample with an odd number of scores? Copyright © Texas Education Agency, 2012. All rights reserved.

The Mode• 6:00 am 120• 7:00 am 110• 8:00 am 160• 9:00 am 205• 10:00 am 170• 11:00 am 150• 12:00 am 170• 1:00 pm 200• 2:00 pm 170• 3:00 pm 152• 4:00 pm 140• 5:00 pm 130

• 6:00 pm 180• 7:00 pm 100• 8:00 pm 143• 9:00 pm 210• 10:00 pm 161• 11:00 pm 80• 12:00 am 40• 1:00 am 30• 2:00 am 40• 3:00 am 20• 4:00 am 10• 5:00 am 31

The Mean (Average)

Mean (Average)

Number of Scores

Each ScoreSum

Notation: Sample data uses CAPITAL Roman letters


Spreadsheet Formulas

=Sum(B2:B11)/Count(B2:B11)Or

=Average(B2:B11)


Not Enough!! Why?Sample One Sample Two

5.0 8.06.4 1.45.0 6.04.5 1.06.0 10.5

Total: 26.9 Total: 26.9

Mean: 5.38 Mean: 5.38

19

Deviation from the MeanSample One Sample Two

5.0-5.38 = -.38 8.0-5.38 = 2.626.4-5.38 = 1.02 1.4-5.38 = -3.985.0-5.38 = -.38 6.0-5.38 = .624.5-5.38 = -.88 1.0-5.38 = -4.386.0-5.38 = .62 10.5-5.38 = 5.12

Tot. Deviation:

0.0

Tot. Deviation:

0.0

Mean: 5.38 Mean: 5.38That does not work!Copyright © Texas Education Agency, 2012. All rights reserved.

20

Let’s Square ThemSample One Sample Two

(5.0-5.38)2 = .14 (8.0-5.38)2 = 6.86

(6.4-5.38)2 = 1.04 (1.4-5.38)2 = 15.84

(5.0-5.38)2 = .14 (6.0-5.38)2 = .38

(4.5-5.38)2 = .77 (1.0-5.38)2 = 19.18

(6.0-5.38)2 = .38 (10.5-5.38)2 = 26.21

Tot.Variance: 2.47 Tot.Variance: 68.47

Mean: 5.38 Mean: 5.38

Works, but values are exaggerated!

Copyright © Texas Education Agency, 2012. All rights reserved.

Standard DeviationTake the total variances and divide them by N-1. Then take the square root of that.

Sample One Sample Two(2.47/(5-1))^.5 = .79 (68.47/(5-1))^.5 = 4.14

𝑺𝑿=√∑ ( 𝑿 −𝑿 )𝟐

𝑵−𝟏

Standard Deviation of the Sample

Sample MeanScore

Number of Scores

The X subscript only shows the S is for the sample

Do you sum the differences then square them or square the differences then sum them?


Degrees of Freedom

Why do we divide by N-1 instead of just N?N-1 is referred to as Degrees of Freedom. It was decided that df is used because it makes the resulting amount larger by using a consistent methodology….that’s all. You will see it again.


Review Questions• On a sheet of notebook paper (or you can type these up on the

computer), answer the following questions. You may use the PowerPoint presentations, as well as websites and any notes you have acquired to answer the questions, just make sure you complete these ON YOUR OWN!

1. What are some of the main types of CHARTS?2. When and how are those charts normally applied?3. How important are indices?4. Describe what statistics is.5. How can statistics be used to describe a list of data?6. What are the elements of Measuring Central Tendencies of a data

list?7. Explain Variance measurements.8. What do we mean when we refer to Degrees of Freedom?


Student Assignments

• Go to my webpage for statistics:– http://www.libertyisd.net/Page/2574

• Click on the link “Student Activity 3.2a” and complete the assignment. When you have finished, go on to “Student Activity 3.2b” and complete it as well.

http://www.libertyisd.net/Page/2574

http://www.libertyisd.net/Page/2574

Describing Data Using Statistics Statistics and Risk Management Copyright © Texas Education Agency,...

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