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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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…
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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
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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
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Teacher Preparation:
Teacher will:
1.
presentation, and
handouts.
2.
resources and websites.
3.
websites ready.
Review terms in outline,
Locate and evaluate various
Have assignments and
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.
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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
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Provide Assignment sheets and discuss
and answer any questions about
assignment (In class or take homeInstructor’s Option)
VIII.
Tool of Knowledge
A. Statistics: The study of
collecting, organizing, and
analyzing data.
1. For Research
Provided .docx files
3.1a
DescribingData_Visually
3.1b
DescribingData_Visually
2. For Reporting
B. Research Statistics?
C. Descriptive Statistics:
Procedures used to
organize and present data
in a convenient and
communicable form.
Use presentation
DescribingData_Statistically.pttx
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.
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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)
Provided .docx files
3.2a
DescribingData_Statistically
3.2b
DescribingData_Statistically
Provide Assignment sheets and
discuss/answer any questions about
assignment .
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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.
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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.
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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.
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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.
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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.
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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.
B.
C.
D.
E.
Inferential Statistics
Histogram
Data Range
Descriptive Statistics
Pie Chart
7.
8.
9.
10.
11.
__________ The measurement between the low and high raw data score.
__________ A graphical representation of data normally demonstrating the relationship in size between data groups.
__________ Procedures used to organize and present data in a convenient and communicable form.
__________ A graphical representation of data normally demonstrating the relationship in size over a period of time.
__________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
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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
D. All of the above
rather than using words
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
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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
C. Mode
B. Median
D. Variance
24. To make the standard deviation larger, what would you have to do?
A. Change any existing data to values
B. Keep everything the same
closer to the mean
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
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18
Describing Data Test Key
1. B
2. B
3. A
4. A
5. A
6. A
7. C
8. E
9. D
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B
C
B
C
D
B
A
C
A
B
D
C
B
A
D
C
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