Focus on what you learned that made an impression, what may have surprised you, and what you found particularly beneficial and why. Specifically: What did you find that was really useful, or that challenged your thinking? What are you still mulling over? Was there anything that you may take back to your classroom? Is there anything you would like to have clarified? ANSWER THE ABOVE QUESTIONS BASED ON THE DOCUMENTS BELOW Introduction & Goals This week, we will investigate the distribution of a variable and look at ways to best see the key features of a quantitative variable’s distribution. We will look at visualizations of data, including line plots, frequency tables, stemplots, and histograms. We will hone our ability to describe key features of a distribution from visualizations and use them to compare distributions. We will begin to think about ideas for the Comparative Study by brainstorming in our project groups. Goals : Reinforce the idea that data will vary Explain what the distribution of variable is Identify five key features of a distribution: center, spread, shape, clusters & outliers Identify and create appropriate displays for categorical and quantitative data in one variable, including bar graphs, line plots, frequency tables, and histograms Analyze distributions using stemplots and histograms Recognize advantages and limitations of histograms Begin to explore technology for use in statistics Begin work on Comparative Study Final Project DOW #2: How Long Is A Minute? In week 1, we gathered data for this week’s DoW, addressing the question: “How long is a minute to an adult?” This week we'll: In investigations 1 & 2, you will analyze the data with dot plots, frequency tables, stemplots, and histograms. In Exercise B2, you will post your initial analysis and interpretation to the discussion board by Wednesday, 10 PM EST and create at least three follow-up posts by Friday, 10 PM EST. In Exercise D2 & E2, you will post your best histogram to the discussion board by Friday, 10 PM EST. Compare the histograms and choose the one you think best represents the distribution by Sunday, 10 PM EST Investigation 1: Seeing the Distribution As we emphasized in Week 1, data varies . This point may seem trivial, but it encapsulates one of the most fundamental concepts of statistics: variability . Statistical Analysis is really a study of the patterns we find within this variation in the data. The pattern(s) in the variation is called the distribution of the variable. Much of statistics focuses on ways to represent and describe the distribution of a variable. Activities A & B in this investigation focus on representing and describing the distribution. Activity C introduces Excel as a tool for looking at a distribution.  Inv 1, Activity A: Patterns in the Variation As we emphasized in Week 1, data varies . This point may seem trivial, but it encapsulates one of the most fundamental concepts of statistics: variability . Statistical Analy.

1. Focus on what you learned that made an impression, what may
have surprised you, and what you found particularly beneficial
and why. Specifically:
What did you find that was really useful, or that challenged
your thinking?
What are you still mulling over?
Was there anything that you may take back to your classroom?
Is there anything you would like to have clarified?
ANSWER THE ABOVE QUESTIONS BASED ON THE
DOCUMENTS BELOW
Introduction & Goals
This week, we will investigate the distribution of a variable and
look at ways to best see the key features of a quantitative
variable’s distribution. We will look at visualizations of data,
including line plots, frequency tables, stemplots, and
histograms. We will hone our ability to describe key features of
a distribution from visualizations and use them to compare
distributions. We will begin to think about ideas for the
Comparative Study by brainstorming in our project groups.
Goals
:
Reinforce the idea that data will vary
Explain what the distribution of variable is
Identify five key features of a distribution: center, spread,
shape, clusters & outliers
Identify and create appropriate displays for categorical and
quantitative data in one variable, including bar graphs, line
plots, frequency tables, and histograms
Analyze distributions using stemplots and histograms
Recognize advantages and limitations of histograms
Begin to explore technology for use in statistics
Begin work on Comparative Study Final Project

2. DOW #2: How Long Is A Minute?
In week 1, we gathered data for this week’s DoW, addressing
the question:
“How long is a minute to an adult?”
This week we'll:
In investigations 1 & 2, you will analyze the data with dot plots,
frequency tables, stemplots, and histograms.
In Exercise B2, you will post your initial analysis and
interpretation to the discussion board by Wednesday, 10 PM
EST and create at least three follow-up posts by Friday, 10 PM
EST.
In Exercise D2 & E2, you will post your best histogram to the
discussion board by Friday, 10 PM EST. Compare the
histograms and choose the one you think best represents the
distribution by Sunday, 10 PM EST
Investigation 1: Seeing the Distribution
As we emphasized in Week 1,
data varies
. This point may seem trivial, but it encapsulates one of the
most fundamental concepts of statistics:
variability
. Statistical Analysis is really a study of the patterns we find
within this variation in the data. The pattern(s) in the variation
is called the
distribution
of the variable. Much of statistics focuses on ways to represent
and describe the distribution of a variable.
Activities A & B in this investigation focus on representing and
describing the distribution.
Activity C introduces Excel as a tool for looking at a
distribution.

3. Inv 1, Activity A: Patterns in the Variation
As we emphasized in Week 1,
data varies
. This point may seem trivial, but it encapsulates one of the
most fundamental concepts of statistics:
variability
. Statistical Analysis is really a study of the patterns we find
within this variation in the data. The pattern(s) in the variation
is called the
distribution
of the variable. Much of statistics focuses on ways to represent
and describe the distribution of a variable.
Whether a variable is categorical or quantitative, two good tools
for looking at the distribution are
a frequency table
and
a dot plot
(also called a line plot). This activity introduces and explores
these two tools.
You should self-pace your work according to your familiarity
with these topics.
Exercise A1: Annenberg Investigations, Session 2
Complete the following investigations about line plots and
frequency tables in your journal.
Line Plot Investigation
(approx. 40 min) (Line Plots and Dot Plots are the same things.
Different sources use different names)
Frequency Tables Investigation
(approx. 40 min)
Bar Graphs and Relative Frequency Tables
(approx. 30 min)
Exercise A2: Analyze DoW #2
In your journal create a frequency table of the variable Time, a
relative frequency table and a dot plot BY HAND. Briefly
describe patterns you see in the distribution for Time.

4. Inv 1, Activity B: Picturing a Distribution
There are key features about a distribution that you need to be
on the lookout for as you make and interpret graphical displays.
Five important features are:
1. The center of the distribution
Center refers to the representative value for the data – a
“typical” or “expected” value. This can be estimated from a dot
plot or histogram; it can also be calculated numerically. There
are three different measures of center:
mean, median, and mode
. We will look at these in more detail in Investigation 2.
2. The spread of the distribution
Spread refers to how variable the distribution is – how spread
out or compact. A dot plot or histogram can provide a good
overall view of spread; boxplots provide another view. There
are many different numerical measures of spread. The simplest
is the
range
, the difference between the maximum and minimum values. We
will study many other measures of spread in the next two weeks.
3. The shape of the distribution
There are countless shapes, but three that occur often are
symmetric, skewed right
(the tail extends to the right of the peak),
and skewed left
(the tail extends to the left of the peak). Another common
shape is uniform (roughly the same height throughout).
4. Peaks or clusters
Peaks are values where the frequency is the highest.
Numerically, this corresponds with the mode (the value(s) that
occur most often). Graphically, there are often one or more
clear areas where the frequency is highest. Clusters are
subgroups in the data; on a graph, they will be separated, and
often have their own peaks.

5. 5. Outliers
Outliers are individual points that are significantly above or
below the “majority” of the data. On a dot plot, we can visually
inspect for possible outliers. There are methods for numerically
identifying outliers as well. We will look at those in the next
two weeks.
Exercise B1
: Watch the video
Picturing Distributions
in the Against All Odds video series at this link:
If you have problems with the video link above please
try this entry point
.
This 30-minute video describes the common features of a
distribution, how to look for them in different displays, and the
significance of each one. Take notes in your journal on the five
key features (listed above) as you watch the video. Pay
particular attention to how you interpret each feature (or
differences in features).
Exercise B2: Interpret DOW #2
Look at the dot plot you made in Exercise A2. In your journal,
describe the key features that you see in the plot. (Some
features may not be present.) Make at least two summary
statements for distribution of Time.
Post these summary statements to the discussion board for DoW
#2 by Wednesday, 10 PM EST.
Review the posts.
Post at least three follow-up comments on the analysis and
interpretation of DoW #2 by Friday, 10 PM EST.
Consider the following as you continue your interpretation of
the data:
What do you see as the key features of the distribution of the
variable Time?
Do you think we'd see different features/patterns if we looked at
the trials separately?
Do you agree on the key features?

6. Inv 1, Activity C: Exploring Technology
Data analysis can be done by hand, and there is particular value
to by-hand analysis for our students who are learning such tools
for the first time. You may reflect on your own experience in
Exercise A1, creating dot plots and frequency tables by hand.
However, technology greatly enhances our ability to represent
data in meaningful ways and understand the patterns in the
variation of the data. Technology allows us shift the focus from
making the graphs to interpreting the data. For these reasons,
we will be using technology in addition to by-hand analysis for
this course. Depending on your security settings for Java, this
may be a
useful applet
. Note: Information on
Java settings
is available.
Exercise C1: Analyzing DoW #2
Use the data from DoW #2. Create a dot plot for the variable
Time in DoW #2. You should make a picture of the dot plot so
you can post if necessary.
A few technical hints:
Please Use unlined white paper
Use a ruler
Make sure to create a good scale and labels
Be sure the dot plot is dark enough so others will be able to
read it online
You can Paste into Word or another application for
sharing. This is useful for Weekly Reflections, Discussion
Posts, and if you are keeping an electronic journal.
Exercise C2: Frequency Tables in Excel
The investigation
is written to be used with Excel, but other spreadsheets work
similarly. Depending on your prior experiences, this
investigation may range from being entirely unnecessary to

7. being not nearly enough. This is a time when you can benefit
greatly from the help of your peers. The exercise is guided, but
it is a chance to explore the menus and options as you work, so
you become familiar with what the spreadsheet can do. Be an
active learner in this investigation.
Discussion: Research Plan Draft
You will work with your assigned group for your Comparative
Study. This group serves a valuable purpose as a peer-review.
You are encouraged to embrace the group, take on each
individual's study as your own, and help each other make the
best choices possible. Statistical studies are difficult to conduct
- many professionals have a hard time employing methods that
avoid bias and gather meaningful data. Data is difficult to
analyze - there are many choices about the best way to analyze
the data in a meaningful way. This group serves as a sounding
board for each of you - the more you put into it, the more you
can get out of it!
Your first task is to brainstorm with your group about the
Comparative Study Project. In 250 words or less, share your
thoughts, ideas, and questions about the final project. Some
things you might consider as you write (do not limit yourself to
these prompts or feel the need to address any/all of them):
What makes a good study?
How might you use your students to gather data?
Do you want to try to use a sampling strategy?
What topics interest you for this project?
What questions do you have about study design and your work
in Investigation 2?
What questions do you have about the final project?
Post your brainstorm to your Group Discussion Board by
Wednesday 10 PM EST.
Make at least two follow-up posts that meaningfully add to the
discussion by Sunday, 10 PM EST.
You will be posting a draft of your project proposal to your

8. Group Discussion Board in
Week 3
by Wednesday at 10 PM EST.
Investigation 2: Stemplots & Histograms
Visual representations of a distribution, when properly
constructed, help you see the patterns in the variation. They
become even more valuable as we work with larger data sets.
Dot plots, like the ones used in Module 2, work well for small
data sets or as a quick “view” of the data. Dot plots do not
provide a “big picture” view of the distribution. Often, the
details seen in the dot plots can distract you from seeing the key
features that define the distribution.
In order to better see the “big picture” of a distribution, we
group the data. This investigation looks at ways to group data to
better identify the key features of the distribution (shape,
center, spread, clusters, outliers).
In Activities D & E, we look at stem plots and histograms for
this purpose.
Inv 2, Activity D: Stem Plots and Histograms
Stemplots and Histograms are visual displays of the
distribution. Much like a dot plot, they display the frequency of
each outcome vertically (through height). Unlike a dot plot,
stem plots and histograms group data (by 5’s, 10’s or other
meaningful grouping) in order to provide a big picture of the
shape, center, and spread of the data. The following exercises
introduce and explore stem plots and histograms.
Exercise D1
: Complete the following two activities from the Annenburg
series in your journal. They introduce you to stemplots and
histograms, with an emphasis on how to construct each one and
the ways in which they are meaningful.
Stemplots

9. (55 min)
Histograms
(30 min)
Exercise D2: Analyze DoW #2 By Hand
Make a stem plot for the variable Time. In your group, each
member should select and post a different interval width he or
she will use in making the histogram. Using your interval width,
create a histogram for the variable Time.
Post the histogram to the DB thread for Exercise D2/E2 by
Friday, 10 PM EST.
Inv 2, Activity E: Histograms with Technology
In Activity D, you saw some examples of how changing the
width of the intervals in a histogram can affect the patterns you
see in the distribution. This fact about histograms means that
the analyst making the histogram must use his/her judgment to
create a histogram that represents the distribution well.
When the width of the intervals is too small
, the histogram will look just like a dot plot. It will show all the
variations in the data, and it does not highlight significant
patterns in the distribution.
When the width of the intervals is too large
, all variation is lost in one or two bars. Key features of the
distribution are no longer visible.
Somewhere in between is an optimal interval width
, one which smoothes over the less significant variations in the
data, while highlighting the more significant features of the
distribution. For instance, if there are two distinct clusters in a
distribution, the interval width should not be so large as to
make the histogram one continuous bar graph (with no breaks).
Likewise, the interval would should be large enough to smooth
over less significant variations that detract from the break in the
two clusters.
Because histograms depend on the judgment of the analyst, they
are also subject to

10. manipulation
. Choosing an inappropriate interval width can smooth over
features that might be less desirable. It is our responsibility
(and challenge) in making a histogram to
try to capture all its key features, while smoothing over less
significant variations
.
In this activity,
we will use Excel
to adjust the interval width of the hsitograms for DoW #2. The
goal of the activity is to create a histogram that you believe best
represents the key features of this data.
Exercise E1: Explore the
Illuminations Histogram
Plotter
. Use the data on the website and try creating some data of your
own.
Exercise E2:
Create the histogram that you think best represents the
distribution of the variable Time in DoW #2. You can copy the
data from Word, etc., into the data box in the Applet. If you use
Word for your data, be sure to include commas.
Post this histogram, with a brief justification of why you think
it is best, to the DB for DoW #2 by Friday, 10 PM EST.
Review the histograms. Compare them and choose which
histogram(s) best represent the key features of distribution.
Post at least two follow-up responses by Sunday, 10 PM EST.
As you discuss, you might:
look back to your discussion of the key features (from Activity
B)
consider whether any of the histograms might be misleading
compare the histograms to the stemplots from Activity D.
Gather Data for DoW #3
In Week 1, your group developed a tool for gathering data on

11. the question:
Does the number of raisins in a ½ oz box of raisins differ for a
generic (store-brand) box of raisins and a name-brand box of
raisins?
Implement your tool and collect the data.
Post the data to the google docs spreadsheet (accessible via the
course menu) by Sunday, 10 PM EST.
Week 2 B2:DOW #2Post:
RE: Week 2 B2:DOW #2
Author:
Access the profile card for user: Nerlande Monfort
Nerlande Monfort
Posted Date:
July 10, 2014 12:13 PM
Status:
Published
Time variable is distributed around the ‘expected’ (known)
value and the subsequent observation have a reversing behavior
towards 60s.
There would be differences in patterns if the trials were looked
at separately. This is because the participant would not have a
reference point to act as his error correction basis.
I agree on the key features. Individuals know that a minute has
60s. That is why every subsequent observation is reverting
towards the known value.
Tags:
None
Reply
Quote
Mark as Unread

12. [removed]
Thread:
Week 3 Research Draft
Post:
RE: Week 3 Research Draft
Author:
Access the profile card for user: Nerlande Monfort
Nerlande Monfort
Posted Date:
July 8, 2014 10:13 PM
Status:
Published
I think what makes a good study is something that gives
meaningful results. That is where I am having the biggest
problem. I have three ideas that I will share but I am not sure
how meaningful they are, just interesting.
My first idea was to see if there is a difference between whether
more men or more women hold the door for the person behind
them. I also thought about maybe an adult/teenager twist to it. I
thought I would sit at the mall at the food court entrance, which
has the biggest amount of traffic, and collect my data. I am not
sure how long I should collect for yet or to be honest whether
this is a study worth doing. What can I extract from this study
that would be useful?
My second idea was to study whether or not boys show a
significant height difference from girls in a specific grade
level. I could also choose two grade levels to collect data on
and compare if there is a difference. This could prove
interesting because my guess is that I would see a difference if I
chose a 1
st
grade class and a 6
th

13. grade class.
Waiting for your reply,