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Copyright © Texas Education Agency, 2012. All rights reserved. 1 Statistics and Risk Management Describing Data Performance Objective: After completing this lesson, the student will understand the importance and demonstrate competencies of being able to chart and describe collected data using basic charting and statistical methodologies. Approximate Time: When taught as written, this lesson should take 8-10 days to complete. Specific Objectives: The student will discuss the importance of visual presentations. The student will see and understand the basic types of charting and graphs used The student will explain what is the appropriate chart for a collected set of data The student will understand the importance of chart and graph indices. The student will understand some basic terms and concepts of statistics. The student will be able to identify basic descriptive values relating to data lists. The student will be able to calculate and compute Measures of Central Tendencies relating to data lists. The student will be able to understand and compute variances and standard deviations relating to data lists This lesson corresponds with Unit 5 of the Statistics and Risk Management Scope and Sequence.

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

Statistics and Risk Management Describing Data

Performance Objective: After completing this lesson, the student will understand the importance and demonstrate competencies of being able to chart and describe collected data using basic charting and statistical methodologies.

Approximate Time: When taught as written, this lesson should take 8-10 days to complete.

Specific Objectives:

The student will discuss the importance of visual presentations.

The student will see and understand the basic types of charting and graphs used

The student will explain what is the appropriate chart for a collected set of data

The student will understand the importance of chart and graph indices.

The student will understand some basic terms and concepts of statistics.

The student will be able to identify basic descriptive values relating to data lists.

The student will be able to calculate and compute Measures of Central Tendencies relating to data lists.

The student will be able to understand and compute variances and standard deviations relating to data lists

This lesson corresponds with Unit 5 of the Statistics and Risk

Management Scope and Sequence.

Copyright © Texas Education Agency, 2012. All rights reserved. 2

TEKS Correlations: This lesson, as published, correlates to the following TEKS for Describing Data. Any changes/alterations to the activities may result in the elimination of any or all of the TEKS listed. 130.169 (c)(6)(E) … analyze data presented in frequency distributions, histograms, and ogives … 130.169 (c)(6)(F) … construct and use descriptive indices … 130.169 (c)(6)(C) … generate a spreadsheet to collect, collate, organize, and analyze quantitative data… 130.169 (c)(6)(D) … use spreadsheets and graphical techniques to present data in a manner that is understood by and meaningful to colleagues and clients… InterdisciplinaryTEKS: English: 110.31 (C) (21) (B) … organize information gathered from multiple sources to create a variety of graphics and forms (e.g., notes, learning logs)… 110.31 (C) (22) (B) …evaluate the relevance of information to the topic and determine the reliability, validity, and accuracy of sources (including Internet sources) by examining their authority and objectivity… 110.31 (C) (23) (C) … use graphics and illustrations to help explain concepts where appropriate…

Copyright © Texas Education Agency, 2012. All rights reserved. 3

110.31 (C) (23) (D) … use a variety of evaluative tools (e.g., self-made rubrics, peer reviews, teacher and expert evaluations) to examine the quality of the research…

Math: 111.36 (C) (4) (A) … compare theoretical and empirical probability; 111.37. (C) (3) (B) … use probabilities to make and justify decisions about risks in everyday life

Occupational Correlation (O*Net - http://www.onetonline.org/)

Precision Agriculture Technician 19-4099.02 Similar Job Titles: Crop Specialist, Nutrient Management Specialist, Precision Agriculture Department Manager, Precision Agronomist, Precision Farming Coordinator Tasks:

Collect information about soil or field attributes, yield data, or field boundaries, using field data recorders and basic geographic information systems (GIS).

Create, layer, and analyze maps showing precision agricultural data, such as crop yields, soil characteristics, input applications, terrain, drainage patterns, or field management history.

Document and maintain records of precision agriculture information.

(Soft) Skills: Active Listening; Critical Thinking; Speaking; Problem Solving

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Instructional Aids: 1. Display for presentation, websites for assignments and class

discussion 2. Assignment Worksheets 3. Supporting Spreadsheets

Materials Needed: 1. Printer paper 2. Assignments and website information ready to distribute to

students.

Student projects will be displayed to increase interest in Statistics

Equipment Needed: 1. Computer with presentation and Internet Access 2. Computers for Students to Conduct Research and Collect Data

for Projects

Copyright © Texas Education Agency, 2012. All rights reserved. 5

References: Statistics By the Numbers

Statistics By the Numbers features information about statistics and the how

they are calculated. A sample math problem defines and walks through the

steps for determining mean, medium, mode, range, and standard deviation.

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

Khan Academy: Statistics

Kahn Academy’s Statistics page offers a wide variety of instructional videos for

various statistics lessons. Some of these video lessons include: Mean Median

and Mode, Range and MidRange, Reading Pictographs, Reading Bar Graphs,

Reading Line Graphs, reading Pie Graphs, and more.

http://www.khanacademy.org/math/statistics

The University of Sheffield

(MASH) Mathematics and statistics help, including videos and problems to

solve.

http://www.mash.dept.shef.ac.uk/VarianceandStandardDeviation.html

Ogive

Use arthitecture to explain the ogive curve.

http://curvebank.calstatela.edu/ogive82/ogive82.htm

Copyright © Texas Education Agency, 2012. All rights reserved. 6

Teacher Preparation: Teacher will:

1. Review terms in outline, presentation, and handouts.

2. Locate and evaluate various resources and websites.

3. Have assignments and websites ready.

Learner Preparation: Break the boring barrier. Statistics can be fun and definitely

interesting. Find examples the student might find interesting;

candidate polling, drug testing results, exam grades, and wages

for various careers.

Introduction: STUDENTS will watch the Unit video found here: Introduction

http://jukebox.esc13.net/untdeveloper/Videos/Introduction.mov

Describing Data http://jukebox.esc13.net/untdeveloper/Videos/Describing%20Data.mov

STUDENTS will take the practice test and review using the Key, found in Common/Student Documents. EXHIBIT: Excitement for Statistics and Learning

INTRODUCE: Statistics afford an opinion some credence and can turn an opinion into accepted knowledge.

ASK: Ask students to express some opinions on a

wide range of topics and then challenge them to prove their opinion.

Copyright © Texas Education Agency, 2012. All rights reserved. 7

I. The Visual Advantage A. Easier to make

comparisons. B. Easier to draw conclusions C. A picture is worth a 1000

words. II. Been Around for a While III. Pie Charting

A. Great for Small Number of Groups with Large Variances.

IV. Histogram Charting A. Better when Time is

involved. B. Data is Grouped and placed

along an Axis representing Time.

V. Scatter Charting A. Used to look for

relationships between two Variables or potential Clustering

B. Good for seeing a Correlation or Cluster.

C. Ogive Charting D. Utilizes a line to connect

data. E. When used correctly it can

predict values between and beyond.

VI. Descriptive Indices A. Indices are used to Identify

Groups in Comparison Studies.

VII. Descriptive Scales A. Nominal B. Ordinal C. Interval D. Ratio

Use presentation

DescribingData_Visually.pttx

Copyright © Texas Education Agency, 2012. All rights reserved. 8

Provide Assignment sheets and discuss

and answer any questions about

assignment (In class or take home-

Instructor’s Option)

VIII. Tool of Knowledge

A. Statistics: The study of collecting, organizing, and analyzing data.

1. For Research 2. For Reporting

B. Research Statistics? C. Descriptive Statistics:

Procedures used to organize and present data in a convenient and communicable form.

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

IX. When did this come about? A. We find Statistical

Information (State of Things) in 1749.

B. By the 18th century, the term "statistics" designated the systematic collection of demographic and economic data by states.

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

Provided .docx files

3.1a

DescribingData_Visually

3.1b

DescribingData_Visually

Use presentation

DescribingData_Statistically.pttx

Copyright © Texas Education Agency, 2012. All rights reserved. 9

Data Types E. Qualitative Data F. Quantitative Data

1. Discrete data 2. Continuous data

• Sample Measurements A. Count: Number of Sores B. Range/Low/High: The

Extreme Values • Measures of Central Tendencies

A. Mode: The most Repeated Score

B. Median: The Score(s) in the Middle

C. Mean: The Average of all Scores (A Building Block of Statistics)

• The Mean (Average)

• Spreadsheet Formulas =Sum(B2:B11)/Count(B2:B11)Or =

Average (B2:B11) Not Enough ! Why?

Deviation from the Mean

• Variance • Standard Deviation • Take the total variances and

divide them by N-1. Then take the square root of that.

• Degrees of Freedom • Why do we divide by N-1

instead of just N? • N-1 is referred to 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.

• Spreadsheet Formula =STDEV.P(B2:B11)

Provide Assignment sheets and discuss/answer any questions about assignment .

Provided .docx files

3.2a

DescribingData_Statistically

3.2b

DescribingData_Statistically

Copyright © Texas Education Agency, 2012. All rights reserved. 10

Guided Practice: See assignments.

Independent Practice: Review document “Spreadsheets for Statistical Purposes” – in Common Documents. See assignments.

Review: Question: What are some main types of Charts?

Question: When and how are those charts normally applied?

Question: How important are indices?

Question: Describe what statistics is?

Question: How can statistics be used to describe a list of

data?

Question: What are the elements of Measuring Central

Tendencies of a data list?

Question: Explain Variance measurements?

Question: What do we mean when we refer to Degrees of

Freedom?

Informal Assessment: Instructor should observe student discussion and monitor interaction.

Formal Assessment: Completion of provided assignments using included rubrics for grading.

Copyright © Texas Education Agency, 2012. All rights reserved. 11

Student Assignment

3.1a Describing Data Visually Key

Name: ____________________

There will be times in your career, especially if you working in

management where you will have to present data at a meeting.

Understanding how to create and interpret charts and graphs will be

essential in presenting your viewpoint.

Let’s just start out by finding charts and graphs created by others. See if

you can find some interesting ones that you can see what is being

presented and why you think it was important enough for someone to

create the chart or graph.

On the Web find examples of a pie chart, a bar graph, and a histogram.

Import them into a word processing document and then proceed to

explain what the chart is demonstrating. In addition, describe what

indices are used.

Import these images into a presentation slide format and be prepared to

explain to the class what the chart or graph is showing and why it

interested you.

Answers will vary.

Copyright © Texas Education Agency, 2012. All rights reserved. 12

Student Assignment

3.1b Describing Data Visually Key

Name: ____________________

Using the spreadsheet provided, 3ss_DescribingDataVisually.xlsx,

examine the constructed charts and change the data values to see how

the visual representation changes.

One each of the charts describe what happens as you change the data,

be specific.

Discussion finding will vary.

Copyright © Texas Education Agency, 2012. All rights reserved. 13

Student Activity

3.2a Describing Data Statistically Key

Name: _____________________

Using the spreadsheet provided, 3ss_DescribingDataVisually.xlsx, examine the

Statically Describing Data page and change the data values in column “B” to see

how the Descriptive Results change in column “E”.

To change the mean to a larger value what will you generally have to do to the

data?

ANSWER: Increase any of the existing data elements values or add new elements

of values larger than the mean.

To change the standard deviations to a smaller number what will you have to do to

the data?

ANSWER: Change any of the existing data elements to values closer to the mean.

To make the standard deviation larger what would you have to do?

ANSWER: Change any of the existing data elements to values further away from

the mean.

To make the standard deviation larger while keeping the mean unchanged what

would you have to do?

ANSWER: Change any of the existing data elements to values further away from

the mean. However, for each value above the mean you would have to change an

element to go below the mean in the same amount.

Copyright © Texas Education Agency, 2012. All rights reserved. 14

Student Activity

3.2b Describing Data Statistically Key

Name: _____________________

Your instructor posted the grades for an important exam you took.

The possible range of exam points was 0 to 100 for 50 students

The Mean Score was 80 with a Standard Deviation of 5

The instructor said anyone a scoring higher than +1 STDDEV would get

a “B” and anyone scoring higher that +2 STDDEV would get an “A”.

What would be the minimum score you would need to get to get an “A”?

Explain how you figured out that score you needed.

ANSWER:

Possible: 0 to 100 Points Mean = 80 SD=5

-2 -1 M +1 +2

70 75 80 85 90

If I earned a 90 I would receive an “A”. That is the Minimum.

Copyright © Texas Education Agency, 2012. All rights reserved. 15

Name:_____________________________ Date: _______________ Class:__________________

UNIT 3 DESCRIBING DATA TEST

TRUE and FALSE:

1. The measurement between the low and high raw data score is the Qualitative Data.

A. True B. False 2. Ogive charting doesn’t use lines to connect data.

A. True B. False 3. The study of collecting, organizing and analyzing data is called Statistics.

A. True B. False 4. A scatter graph is a type of mathematical diagram using Cartesian coordinates to display values for 2 variables for a set of

data.

A. True B. False 5. Qualitative and Quantitative Data are two forms of data types.

A. True B. False 6. Utility Bills and Sale Commissions are examples of indices.

A. True B. False

MATCHING:

A. Inferential Statistics

B. Histogram

C. Data Range

D. Descriptive Statistics

E. Pie Chart

7. __________ The measurement between the low and high raw data score.

8. __________ A graphical representation of data normally demonstrating the relationship in size between data groups.

9. __________ Procedures used to organize and present data in a convenient and communicable form.

10. __________ A graphical representation of data normally demonstrating the relationship in size over a period of time.

11. __________Procedures employed which arrive at broader conclusions or inferences about populations on the basis of

samples.

MULTIPLE CHOICE:

12. The supporting chart legends used to describe variables and measurement.

A. Data Range B. Indices C. Variance D. Standard Deviation

13. This type of chart is good for seeing a correlation or cluster and looks for relationships between two variables.

A. Histogram B. Ogive Chart C. Scatter Chart D. Pie Chart

Copyright © Texas Education Agency, 2012. All rights reserved. 16

Name:_____________________________ Date: _______________ Class:__________________

14. This type of chart is better when time is involved. Data is grouped and placed along an axis representing time.

A. Ogive Chart B. Scatter Chart C. Pie Chart D. Histogram

15. Which chart is a graphical representation of data using a line to connect scores illustrating continuity and predictable

outcomes?

A. Pie Chart B. Ogive Chart C. Scatter Chart D. Histogram

16. This type of descriptive scale refers to categorically discrete data.

A. Nominal B. Ordinal C. Interval D. Fiscal

17. The _____ is the overall group of subjects to which the research will apply.

A. Sample B. Data Set C. Population D. Control

18. The _____ is a smaller, more practical, group size that represents the larger population.

A. Sample B. Control C. Data Set D. Population

19. This kind of charting is great for a small number of groups with large variances.

A. Histogram B. Pie Chart C. Scatter Chart D. Ogive Chart

20. Which of the following are visual advantages of charts?

A. Easier to make comparisons B. Easier to draw conclusions C. Simplifies how you see information

rather than using words D. All of the above

Use the following chart to answer questions 21-22.

The histogram shows the heights of 21 students in a class, grouped into 5-inch groups.

21. How many students were less than or equal to 60 inches tall? A. 4 B. 6 C. 10 D. 15

Copyright © Texas Education Agency, 2012. All rights reserved. 17

Name:_____________________________ Date: _______________ Class:__________________

22. How many students were greater than or equal to 75 inches tall? A. 3 B. 1 C. 4 D. 0

23. The formula shown is used to calculate what?

A. Mean B. Median C. Mode D. Variance

24. To make the standard deviation larger, what would you have to do? A. Change any existing data to values

closer to the mean B. Keep everything the same

C. Multiply your standard deviation value D. Change any existing data to values further from the mean

25. Scores were posted for the recent test taken in Statistics & Risk Management. The average score was 70 with a standard

deviation of 5. The instructor said anyone scoring less than a -1 would get a D and anyone scoring +1 would get a C. What

grade would someone get with a +2 standard deviation? A. F B. D C. B D. A

Copyright © Texas Education Agency, 2012. All rights reserved. 18

Copyright © Texas Education Agency, 2012. All rights reserved. 19

Describing Data Test Key

1. B

2. B

3. A

4. A

5. A

6. A

7. C

8. E

9. D

10. B

11. C

12. B

13. C

14. D

15. B

16. A

17. C

18. A

19. B

20. D

21. C

22. B

23. A

24. D

25. C