WELCOME & OVERVIEW
 Examine
Next Generation Sunshine State
Benchmarks related to Measures of Central
Tendency
 Administer Pretest
 Introduce the module objectives
 Developmental Activities: Measures of
Central Tendency – Mean, Mode, Median
Vocabulary development, problem solving,
technology, error analysis/misconceptions
 Review
content: Journal entry
NEXT GENERATION SUNSHINE
STATE STANDARDS
 MA.6.S.6.1:
Determine the measures of central
tendency (mean, median, mode) for a given set of
data.
 MA.6.S.6.2: Select and analyze the measures of
central tendency to represent, describe, analyze,
and/or summarize a data set for the purposes of
answering questions appropriately
 MA.7.S.6.1: Evaluate the reasonableness of a sample
to determine the appropriateness of generalizations
made about the population.
 MA.8.S.3.2: Determine and describe how changes in
data values impact measures of central tendency.
OBJECTIVES

1.
2.
3.
4.
5.
6.
Participants will:
Review the vocabulary related to measures of central
tendency (MA.6.S.6.1)
Determine the measures of central tendency (mean,
median, mode) for a given set of data. (MA.6.S.6.1)
Identify problem solving strategies that may be used to
develop understanding and familiarity with measures of
central tendency. (MA.6.S.6.2)
Explore how changes in data values and extreme values
affect measures of central tendency. (MA.7.S.6.1;
MA.8.S.3.2)
Explore the use of technology and other instructional
strategies that may be used to facilitate student
understanding of measures of central tendency.
(MA.6.S.6.2)
Develop the ability to communicate mathematically
through journal writing and problem solving.
(MA.6.S.6.2)
?Measures of Central
Tendency?
Brainstorming
 What
are measures of
central tendency?
 How
are they used in everyday
situations?
 Measure
of central tendency are used to
describe the typical member of a
population.
 Depending on the type of data, typical
could have a variety of “best” meanings.
 Real life examples:
 Most
children in the 8th grade are 13 yrs
old.
 The median annual family income is
$39,600
 Ft. Lauderdale’s average rainfall for the
month of July is 6.6 inches.
3 MEASURES OF CENTRAL
TENDENCY
 Mean
– the arithmetic average. This is
used for continuous data.
 Median – a value that splits the data into
two halves, that is, one half of the data is
smaller than that number, the other half
larger. May be used for continuous or
ordinal data.
 Mode – this is the category that has the
most data. As the description implies it is
used for categorical data.
DEVELOPING VOCABULARY
POWER
Activity
Describe and complete an activity that may be
used to build student vocabulary power.
Terms: central tendency, mean, median, mode,
variability, range, set of data, frequency table,
numerical data, categorical data, outliers, line plot,
circle graph, continuous data,
categorical data, common, middle,
most often
Access the eglossary@glencoe.com
USING MANIPULATIVE MATERIALS
“Manipulating the physical model not
only helps [children] understand the
formula but also promotes retention.”
“Simply being able to state the algorithm
for finding these statistics is not enough.
To support the development of data
sense, each of these should be developed
meaningfully through concrete activities
before introducing computation.
(Reys, et. al. 2009; p. 395)
MODELS FOR FINDING
THE MEDIAN OF AN ODD/EVEN AMOUNT
OF DATA IN A GIVEN SET
Find the median of 2, 3, 4, 2, 6.
Participants will use a strip of grid
paper that has exactly as many boxes as
data values. Have them place each
ordered data value into a box. Fold the
strip in half. The median is the fold.
USING MANIPULATIVE MATERIALS
INTERLOCKING CUBES
 Arrange
interlocking/Unifix cubes together in
lengths of 3, 6, 6, and 9.
 Describe how you can use the cubes to find the
mean, mode, and median.
 Suppose you introduce another length of 10
cubes. Is there any change in
i) the mean,
ii) the median,
iii) the mode?
FINDING THE MEAN LENGTHS:
USING ADDING MACHINE TAPE
 Activity:
Return test scores to students
on pieces of adding machine tape. The
length of each strip is determined by the
score (88 cm, and 64 cm). Tape the 2
strips of paper together (add). Write out
the addition part on the back - 88, 8…
Fold this in half (divide by 2).
 Try
doing it with 3 pieces of strips. Does
it work? Explain.
VISUALIZING THE MODE
Category
4 has
the highest bar.
Category
4 is
the mode.
The
mode is the
class, not the
frequency.
Series 1
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Series 1
MEAN MEDIAN & MODE
Purpose: Reinforce concepts through
songs.
Click in the link
http://www.youtube.com/watch?v=uyd
zT_WiRz4
 Would
you use this tool in the classroom?
Why/why not? Explain.
USING POEMS, RHYMES & MNEMONICS
Cheers: Mean, Median, and Mode
Mean (Say in really mean voice and face throughout!)
Add all the numbers (Have hand go from waist to neck
in increments.)
And Divide! (Have same hand slice across the neck!)
Median …Middle
Order numbers least to greatest (motion hand left to
right)
Find the middle. (move both hands to middle and clap)
When I say mode you say Most
Mode….Most
Mode….Most!
Mode is the number that appears most often
Mode…Most often
Mode…Most often!
UNDERSTANDING THE MEAN
 The
mean is located between the extreme
values.
 The mean is influenced by values other than
the mean.
 The mean does not necessarily equal one of
the values that was summed.
 The mean can be a fraction.
 When you calculate the mean, a value of 0, if
it appears, must be taken into account.
 The mean value is representative of the
values that were averaged.
CALCULATING THE MEAN
(ARITHMETIC AVERAGE)


To find the mean:
add all of the values,
then divide by the
number of values.
A student’s score on 4
math tests are: 8, 5, 9,
6. Calculate the mean
score.

Sum of all values
8 + 5 + 9 + 6 = 28
Number of values = 4

Mean = 28 ÷ 4 = 7

Mean score on the math
test is 7
Check!
7
8, 5, 9, and 6 or 5, 6, 8, 9
THE MEDIAN
 The
median is a number chosen so that half
of the values in the data set are smaller than
that number, and the other half are larger.
 To find the median



List the numbers in ascending order
If there is a number in the middle (odd number of
values) that is the median
If there is not a middle number (even number of
values) take the two in the middle, their average is
the median
FINDING THE MEDIAN

To find the median:
list all of the values, in
order of size. Select
middle value(s)

5,
A student’s score on 4
math tests are: 8, 5, 9, 6.
Calculate the median
score.
M E
A N
6,
6


List values in order of size
8,
9
8
Find the average of the
selected values.
(6 + 8) ÷ 2 = 7
Median score on the math
test is 7
Check!
7
8, 5, 9, and 6 or 5, 6, 8, 9
Group Activity
Finding Mean, Median and Mode for data
sets
 Figure out the mean, median, mode,
range, and outlier using a group/card
activity
Discuss the various measures.
 Materials: 4 sets of activity cards (Nine
4 x 4 Index cards 1, 5, 6, 7, 8, 9, 10, 11,
12, 18) use either 1 or 18 as an outlier;
calculators.
THE MODE
 The
mode is simply the category or value
which occurs the most in a data set.
 If a category has more than the others, it
is a mode.
 Generally speaking we do not consider
more than two modes in a data set. (i.e.
Bi-modal)
 No clear guideline exists for deciding how
many more entries a category must have
than the others to constitute a mode.
OUTLIER EFFECTS ON
MEASURES OF CENTRAL TENDENCY

Give nine different students a card and have them come
to the front of the room and hold their card facing the
rest of the class.
Give the remaining seated students a calculator.
Follow directions on activity sheet.
Discuss how the outlier affects the measures of central
tendency.
PROBLEM SOLVING
Using different Strategies!
Andy’s results on three tests are: 68, 78, and 88.
1. Find the mean and median score.
2. Explain why the mode is of little value.
3. What score would be needed on the next
test to get an average of 81.
4. Describe two different ways you could
determine this score.
INVESTIGATING
DESCRIPTIVE STATISTICS
 Using
technology
WHAT DOES IT MEAN TO
UNDERSTAND THE MEAN?
Plop It!
 Participants
will experiment with the
concepts of mean, median, and mode by
using a bar graph.
 Participants will change parameters and
discover patterns related to mean and
median. They can choose their own focus of
measure, their own quantity, and their own
units.
URL:
www.shodor.org/interactivate/activities/plot/
what.hmtl
USING SPREADSHEETS
MA.8.S.3.2: Determine and describe how changes in
data values impact measures of central tendency.
 Purpose: use technology to calculate mean, mode, and
median of a set of data.
Task: Make a spreadsheet for a given data set and find
the measures of central tendency. (See slide 26 for
data.)
1. Open a new spreadsheet. Create four columns labeled
DATA, MEAN, MEDIAN, and MODE.
2. Enter each allowance amount in the DATA column.
3. In cell B2, enter =Average(A2:A11). In cell C2, enter
=Median(A2:A11). In cell D2, enter =Mode(A2:A11).
Each of these will find the mean, mode and median of
the data set.
 Analyze the results.

Mrs. Jensen’s 7th grade class was surveyed about how
much allowance each student receives each week.
The results are shown in the table.
Use this information to make a spreadsheet for the
data, and find the mean, median, and mode.
15
28
Allowances per week (5)
10
11
9
12.50
12
10
10
15
Analyze the results.
1. What data value is an extreme for the set? Explain
your reasoning.
2. Describe how the measures of central tendency
would change if the extreme value was not included
in the data set.
CHANGES IN DATA VALUES IMPACT ON
MEASURES OF CENTRAL TENDENCY
 Example:
Mrs. Donohue has told her
students that she will remove the lowest
exam score for each student at the end of
the grading period. Sara received grades of
43, 78, 84, 85, 88, 78, and 90 on her exams.
What will be the different between the
mean, median, and mode of her original
grades and the mean, median, and mode of
her five grades after Mrs. Donohue
removes one grade?
COMMUNICATING MATHEMATICS IDEAS
Measures
Central
Tendency
Mode
Mean
Median
Quartile
Range
OBJECTIVES







Examine student misconceptions in statistical thinking.
Use researched information on statistical thinking to create
activities geared at helping students develop better
understanding of averages.
Connect Math and Language Arts by providing activities for
students to develop their vocabulary skills while
simultaneously developing conceptual understandings.
Construct and analyze histograms, stem-and-leaf plots, and
circle graphs.
Make conjectures about possible relationships from data sets.
Identify teacher-specific instructional tools and methods for
graphically displaying data.
Explore web-based educational resources designed to
reinforce learning of graphical displays and measures of
central tendency.
BENCHMARKS
 MA.6.S.6.2:
Select and analyze the
measures of central tendency or variability
to represent, describe, analyze, and/or
summarize a data set for the purposes of
answering questions appropriately
 MA.7.S.6.2: Construct and analyze
histograms, stem-and-leaf plots, and circle
graphs.
 MA.8.S.3.2: Determine and describe how
changes in data values impact measures of
central tendency.
MISCONCEPTIONS
“Many middle graders are able to
calculate averages but their
understanding of the concept of
average is shallow.” (Reys, et al., 2009).
Participants will identify
misconceptions students might have
about statistics.
CONNECTING RESEARCH
AND PRACTICE
Purpose: to review measures of central tendency,
and provide an opportunity for participants to
use research findings to inform their
instructional practices.
 Task:
Participants will read 1 research article on
Measures of Central Tendency.
 Participants will summarize the article and
discuss the main findings as they apply to the
teaching and learning of Measures of Central
Tendency.
DIFFICULTIES IN INTERPRETING
THE MEAN
“Akira read from a book on Monday, Tuesday and
Wednesday. He read an average of 10 pages per day.
Circle whether each of the following is possible or not
possible.”
Possible
Pages Read
Not
Possible
Monday
Tuesday
Wednesday
A
A
a
4 pages
4 pages
2 pages
B
B
b
9 pages
10 pages
11 pages
C
C
c
5 pages
10 pages
15 pages
D
D
d
10 pages
15 pages
20 pages
Outcome:
 Less than 40% answered all 4 choices correctly.
“Many middle graders are able to calculate
averages but of understanding of the concept of
average is shallow.” (Reys, et al., 2009, p. 396).
Remediation Activity
Work with a partner to develop an activity to
help students better understand the concept of
average.
Present your activity to the class with a
rationale for selecting this activity.
MISCONCEPTION
ABOUT
THE MEDIAN
 Problems
involving finding the median
Problem: When finding the median of
an even-numbered set of data, some
students use the mean the data
instead of the mean of the two middle
numbers.
Describe an activity that may be used
to help students overcome this
WORD FRAME: DIFFERENCES &
SIMILARITIES
Similarities
Differences Diagram/Pictur
e
Names
Show data
Line plot
in different
Using a Line ways
Line graph
The line is
used
differently
FOCUS QUESTION/ACTIVITY
 How
are statistical displays helpful to
us in our everyday lives?
Make a list of the different types of
graphs that you know. Select one of the
graphs, and write about a situation in
which you will use that graph to display
data.
MISLEADING GRAPHS
Participants compare two Bar graphs with
the same data, and discuss why one may be
misleading.
ERROR ANALYSIS
 To
look at a student’s sleeping pattern a
student made a Line Plot of the number
of hours he slept each night for one
week. Describe the student’s error and
tell which display he should have made.
USING TECHNOLOGY
CONSTRUCT & ANALYZE
HISTOGRAMS AND CIRCLE GRAPHS
Group Activity
 Assign groups of no more than 4per group.
Participants use the computer to get a feel for
the technology and discuss the usability and
benefits of including such tools in the 6-8
math curriculum.
 Circle grapher, and histogram tool
http://illuminations.nctm.org/ActivityDetail.
aspx?
CHOOSING AN APPROPRIATE
DISPLAY
WHY ME!
Which graph would you use to
compare the number of red folders
sold by two stores in one week?”
Series 3
Category 4
Category 3
Series 2
Category 2
Series
2
10
8
6
4
2
0
Category 1
Series
1
Categor…
Categor…
Categor…
Categor…
5
4
3
2
1
0
CONVERTING A BAR GRAPH
INTO A CIRCLE GRAPH
 Instruction:
Copy a Bar graph. Write a label on
each bar. Cut our each bar from the graph.
Tape the ends together (no overlaps) to form a
circle.
 Place the circle on a sheet of paper. Trace the
circle. Mark where each bar begins and ends
around the circle.
 Mark the center of the traced circle. Draw in a
radius from each of the lines marked on the
circle.
 Color the sections of the circle. Label each
section, and title your graph.
DATA ANALYSIS &
MEASURES OF CENTRAL TENDENCY
ACT IT OUT: STEM AND LEAF
PLOTS

Problem Solving Strategy: Act it out
Given the data set: 7, 51, 25, 47, 42, 55, 50, 26, 44, 55, 26,
33, 39, participants will:
Copy the numbers unto individual index card.
Sort the cards into piles based on place value. (Stem
value)
Note what they have in common
Cut one of the stem, place it on a sheet of paper or the
table. Cut the remaining leaves with this stem. Add the
leaves to the leaf section of the plot.
Repeat for each of the piles.
Discuss the plot by examining the lowest and highest
scores, the lengths of each leaf, gaps, tapers, and the
median and modal values.
STEM AND LEAF PLOT
Activity:
 Create the plot from the information presented
below.
An example of a stem-and-leaf plot for the data
set (34, 30, 38, 42, 67, 68, 68, 56, 54, 34, 82,
and 85) is as follows: Legend: 3|234
 Discuss
what is the
median of the data set?
 mode of the data set?

REVIEW EXERCISE
 What
does the data represent?
 What
type of central tendency would you use
to represent it? Why? Include each of the
measures in your justification.
 Sketch
the type of graph you would make to
represent the data set.
 How
can the data representation influence
conclusions?
THANK YOU FOR
COMPLETING
MODULE 46.2
BLOCK 46
MODULE 3
L
MODULE OBJECTIVES
Participants will:
 Discuss what is meant by the term “measures of
variation”
 Develop vocabulary activities to reinforce understanding
of concepts of measures of variation
 Examine the 5 point summary or key (Quartiles)
 Select, organize, construct, and analyze Box and Whisper
plots (single and double)
 Select, organize, and construct scatter plots and lines of
best fit for given data sets
 Examine misconceptions student have about scatter plots
 Make conjectures about possible relationships in the data
 Use technology to create measures of variation
BENCHMARKS
MA.6.S.6.1: Determine the measures of central tendency
(mean, median, mode) and variability (range) for a given
set of data.
 MA.6.S.6.2: Select and analyze the measures of central
tendency or variability to represent, describe, analyze,
and/or summarize a data set for the purposes of
answering questions appropriately
 MA.7.S.6.1: Evaluate the reasonableness of a sample to
determine the appropriateness of generalizations made
about the population.
 MA.8.S.3.1: Select, organize and construct data displays,
including box and whisker plots, scatter plots, and lines
of best fit to convey information and make conjectures
about possible relationships.
 MA.8.S.3.2: Determine and describe how changes in
data values impact measures of central tendency.

VOCABULARY POWER
 Participants
create a graphic organizer to
identify the five key measures of variation.
Word
Definition
Interquartile Range
Range between upper
and lower quartiles
What It Is
2,3, 4, 5, 6,7, 8
What It Is Not
2, 3, 4, 5, 6, 7, 8
5 … median
6 … range
7–3=4
USING A WORD WEB
 Participants
will use a Word Web
template to fill in the vocabulary words.
(range, lower quartile, outliers, upper
quartile, quartiles, interquartile,
measures of variation.
Examine web and ask:
 Why are the range and outlier separated
from the quartiles?
MEASURE OF VARIATION
 Used
to describe how much the data is
spread out.
 The variation in a data set is easily
examined in a line plot or graph
 The range is a simple measure of
variability. It tells the difference
between the highest and lowest values in
a given set of data.
 Why measure spread?
USING THE RANGE

Complete the table. Can you use the mean, mode, or
median to compare the two players’ performance? Why/why
not?
Player Points scored
in the last 10
games
1
16, 20, 20, 18,
22, 24, 20, 20,
20, 20
2
10, 2, 20, 36, 4,
20, 38, 0, 30, 40
Mean Median Mode
RANGE & QUARTILES
Mean, the median and the mode are
measures of the central tendency of
a set of data.
However, such measurements
cannot tell us the spread or variation
of the data.
Dispersion is the statistical name for
the spread or variability of data.
FOLDABLE ACTIVITY: QUARTILES
Median
Lower Quartile
2
3
Upper Quartile
5
7 10
16
Interquartile
Range
11
15

Rewrite the data in order, from smallest length to largest:

Find the median of all the numbers. Notice that since there are 13
numbers, the middle one will be the seventh number:

o
Find the lower
quartile. This is the
middle of the lower
six numbers. The exact
center is half-way
between 8 and 9 ... (8.5)
Find the upper quartile.
This is the middle of
the upper six numbers.
The exact centre is
half-way between 14 and
14 ... which must be 14
Measure of
dispersion
1. Range
Advantage
Only two data are
involved, so it is
the easiest one to
calculate.
Disadvantage
Only extreme
values are
considered which
may give a
misleading
impression of the
dispersion.
It only focuses on It cannot show the
2. Interquartile range the middle 50% of dispersion of the
data, thus avoiding whole group of
the influence by
data.
extreme values.
EFFECTS ON THE DISPERSION
WITH CHANGE IN DATA
 Removal
of a certain from the data.
If the greatest or the least value (assuming both are
unique) in a data set is removed, then
(1) the range will decrease;
(2) the inter-quartile range may increase or decrease.
If a zero value is inserted in a positive data set, then
1. the range will increase;
2.
the inter-quartile range may increase of decrease
BOX AND WHISKER PLOTS
A box and whisker graph is
used to display a set of data so
that you can easily see where
most of the numbers are.
http://nlvm.usu.edu/en/nav/frame
s_asid_200_g_3_t_5.html
Line Plot: Quartiles
What are the median, lower and upper quartiles?

1
Median
Upper Q
Lower Q

x x x x
x
x
x
x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Where do the numbers cluster together and where do
they spread out? Explain.
Where are the extremes located in relation to the
clustered data?
A BOX-AND-WHISKER PLOT

It illustrates the spread of a set of data. It provides a
graphical summary of the set of data by showing the
quartiles and the extreme values of the data.
The difference between
the two end-points of
the line (represented by
the highest and lowest
marks) is the range.
The length of the box is
the inter-quartile range.
Double Box and Whisker Plots
Alfonso's bowling scores are 125, 142, 165, 138, 176,
102, 156, 130, and 142. Make a box-and-whiskers plot
of the data. The box and whiskers plot below
represents the bowling scores of Anna. Compare the
bowling scores of Alfonso and Anna. Who is a better
bowler?
STEM AND LEAF/BOX AND WHISKER PLOT
Investigation: Drops on a Penny: Graphing Data
http://fcit.usf.edu/FCAT8m/penny1/default.htm
COLLECT THE DATA
1.
Guess how many drops of water a Heads-Up penny
will hold.
2. Count how many drops it will actually hold.
3. Record your data.
GRAPH THE DATA
Create a Stem-and-Leaf plot of the class data.
ANALYZE THE DATA
1. Use the data to calculate the mean, median, mode
and range.
2. Use this data to create a box and whiskers plot.
SCATTER PLOT
It is a scattered plotting of points that may or
may not seem to follow some sort of trend or
pattern.
 What
sort of a trend would they follow?
A fitted line (or line of best fit) of course!
The fitted line is one that is closest to every
point in the plot.
If two points are a ways a part, the line must
compromise and go between them.
LINE OF BEST FIT
 http://illuminations.nctm.org/ActivityDetai
l.aspx?ID=146
 This
activity allows the user to enter a set
of data, plot the data on a coordinate grid,
and determine the equation for a line of
best fit.
 After reading the instruction, click on
Exploration and complete the task.
 Try to explain the changes that occurred
when data was removed?
SCATTER PLOTS
DESCRIBING RELATIONSHIP
 Activity:
(Distribute Activity Sheet)
In groups of three, examine the following
sample scatter plots. Once you have
’thoroughly’ examine them, rank them in order
from strongest to weakest relationship
between the variables. Finally, briefly explain
your selections in the area provided below.
Be ready to present your findings!
EXAMINING RELATIONSHIPS
3 Types of Relationships

ALTERNATIVE ACTIVITY
Draw the graph to show the correlation
between shoe size and height.
This is one of the two things scatter plots
can be used to find the answer to:
 Is there a correlation between the
variables?
 How can we use that correlation to
predict values that we haven’t measured?
ALTERNATIVE INTERNET ACTIVITY
 Participants
will research endangered species such as
the Florida Panther or the peregrine falcon. They will
use technology to create a scatter plot of the
population by year, month, or other time period.
 Participants will answer the following questions:
1. What trends do you notice in the population of this
animal?
2. What measures are being taken to help the animal,
and when did they began?
3. What effect do you think this had on the population
of your animal?
4. Based on the graph and the measures you
researched, what do you predict the population of
your animal to be in ten years?
SCATTER PLOT: MISCONCEPTIONS



Students often fail to learn what situations a newly
learned representation is appropriate for, preferring to
use the first and simplest representations of data they
learn, even in situations where those representations
are not useful (Hancock, Kaput, and Goldsmith, 1992).
Students focused solely on their surface features
rather than their structural or informational
properties (McGatha, Cobb, and McClain, in press)
Students’ misconception due to variable error or
nominalization error.
Variable
Choice Error
places a
nominal or
categorical
variable rather
than a
quantitative
variable along
one axis
Nominal or
Categorical Error
treat a quantitative
variable already
chosen for one axis as
if it were a nominal
variable
THANK YOU & FAREWELL
 We
sincerely thank you
for being creative, and
active participants in
the instructional
sessions. It is the
Team’s wish that you
will incorporate the
ideas technology and
strategies shared in
your professional
practices.
 Great Job!!!
 It’s
your turn to
show what you
know and can do!!
 Best
 See
regards
you in the
classroom soon.
REVIEW EXERCISE: POST TEST
Reflections & Suggestions
RESOURCES
Websites
Journals
Books
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Circle Grapher: http://illuminations.nctm.org/ActivityDetail.aspx?ID=60
CTAP Region 4. 6th Grade Matix: Statistics, Data Analysis and Probability. Retrieved from
http://www.ctap4.net/projects/middle-school-math/matrices/6th-grade-matrix-statistics-data-analysis-andprobability/126-matrices/150-6th-grade-matix-statistics-data-analysis-and-probability.html
eGlossay. Retrieved from http://www.glencoe.com/apps/eGlossary612/landing.php
FCAT 8th grade Math: A staff developmental tool. Retrieved from http://fcit.usf.edu/FCAT8m/default.htm
FCAT example. Retrieved from http://fcit.usf.edu/FCAT8m/penny1/default.htm
Histogram Tool: http://illuminations.nctm.org/ActivityDetail.aspx?ID=78
Justify measure of central tendency. Retrieved from
http://wiki.bssd.org/index.php/S%26P:_Justify_measure_of_central_tendency
Lessons. Retrieved from http://teachers.net/lessons/posts/3789.html
Math Standards. Retrieved from http://www.floridastandards.org/Resources/PublicPreviewResource1347.aspx
Mean Median & Mode Math Learning Upgrade. Retrieved from
http://www.youtube.com/watch?v=uydzT_WiRz4
Measures of Central Tendency (Middle School). Retrieved from
http://www.beaconlearningcenter.com/lessons/99.htm
Measures of central Tendency. Retrieved from http://croitz.blogspot.com/2009/12/measures-of-centraltendency.html
National Library of Virtual Manipulatives. Box Plot. Retrieved from
http://nlvm.usu.edu/en/nav/frames_asid_200_g_3_t_5.html
NCTM website: http://illuminations.nctm.org/ActivityDetail.aspx?ID=146
Plop It! Retrieved from www.shodor.org/interactivate/activities/plot/what.hmtl
Retrieved from http://www.google.com/search?hl=en&rls=com.microsoft%3Aen-us%3AIEAddress&rlz=1I7ADBF_en&q=What+are+some+of+the+misconceptions+students+have+about+scatterplots&aq=f
&aqi=&aql=&oq=
Scatter Plots: Describing Relationship. Retrieved from
http://www.google.com/search?hl=en&rls=com.microsoft%3Aen-us%3AIEAddress&rlz=1I7ADBF_en&q=What+are+some+of+the+misconceptions+students+have+about+scatterplots&aq=f
&aqi=&aql=&oq=
Baker, R., Corbett, A., Koedinger, K., & Schneider, M. (2002).
A formative evaluation of a tutor for scatterplot generation:
evidence on difficulty factors. Retrieved from
http://users.wpi.edu/~rsbaker/BCKSAIED2003Final.pdf
 Capraro, M., Kulm, G., & Capraro, R. (2005). Middle grades:
Misconceptions in statistical thinking. School Science and
Mathematics,105(4),165 – 175.
 Capraro, R., Kulm, G., Hammer, M., & Capraro, R. (n.d.).
The origin and persistence of misconception in statistical
thinking. Retrieved from
http://www.coe.tamu.edu/~mcapraro/mmcspublished%20articles/PMENA-Misconcep.pdf
 Kraus, S. (2010). Monstrous Methods for Teaching Central
Tendency Concepts. Teaching Statistics, 32(1), 21–23.
 Russo, L., & Passanante, M. (2001). Statistics fever.
Mathematics Teaching in the Middle School, 6(6), 370 – 374.

 Glencoe
McGraw-Hill. (2011). Florida Math
Connects, Course 3 (Teacher ed.). OH: Glencoe
McGraw-Hill.
 Glencoe McGraw-Hill. (2011). Florida Math
Connects, Course 2 (Teacher ed.). OH: Glencoe
McGraw-Hill.
 Glencoe McGraw-Hill. (2011). Florida Math
Connects, Course 1 (Teacher ed.). OH: Glencoe
McGraw-Hill.
 Larson, R., Boswell, L. (2010). Big Ideas MATH,
Florida Teacher ed. PA: Big Ideas Learning.
 Reys, R., Lindquist, M., Lamdin, D., & Smith, N.
(2009). Helping children learn mathematics; Ch.
17, p. 409. NJ: John Wiley & Sons, Inc.