describing data using statistics statistics and risk management copyright © texas education agency,...
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Copyright © Texas Education Agency, 2012. All rights reserved. 1
Describing Data Using Statistics
Statistics and Risk Management
Copyright © Texas Education Agency, 2012. All rights reserved. 2
“Copyright and Terms of Service
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Call TEA Copyrights with any questions you have.
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Tools of Knowledge
Statistics:
The study of collecting, organizing, and analyzing data.• For Research• For Reporting
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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.
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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:
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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.
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Data Types
Qualitative Data Quantitative Data
Discrete data Continuous data
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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
• 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 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
• 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 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
• 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
What about a sample with an odd number of scores? Copyright © Texas Education Agency, 2012. All rights reserved.
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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
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
• 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
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
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Spreadsheet Formulas
=Sum(B2:B11)/Count(B2:B11)Or
=Average(B2:B11)
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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
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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.
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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!
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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?
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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.
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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?
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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.