UNIT : Statistics and Probability
Unit/ Topic Length:
In this unit the students will explore and understand measures of center of data. The students will
then strengthen their understanding by working through some applications of mean, median, and
mode. Then students will review the vocabulary dealing with measurements of variation such as,
max, min, range and interquartile range and mean absolute deviation. Then students will explore
the different ways to display data, through dot plots, histograms, and box plots.
Essential Questions:
 What makes a question a good statistical question?
 How do you determine the best treatment for a given set of data?
 How significant is the result of the treatment of a given set of data in terms of making a
conclusion, a generalization and predictions?
Big Ideas/Enduring Understandings
 The answer to a statistical question is
obtained through the treatment of a
collection of data that exhibits variability.
 Understand that a set of data collected to
answer a statistical question has a
distribution which can be described by its
center, spread and overall shape.
 The measure of the center of data is
obtained in different ways such as the
mean, median and the mode.
 The measure of the variation or spread of
the data is obtained in different ways such
as the range, interquartile range and the
mean absolute deviation.
 The measure of the center and the
measure of the variation are essential to
analyze data.
 Data can be displayed as a dot plot,
histogram, and box plot.
 Data display is essential to organize data.
Guiding Questions:
 Compare a statistical question and a nonstatistical question.
 What are the ways of describing the shape of
a data distribution?
 How do you interpret data by looking at the
overall shape of the data distribution.?
 What is the significance of the measure of
the center of the data?
 How do you measure the center of the
data?(mean or average, median and mode)
 What does the measure of variation or the
spread of the data imply?
 How do you measure the variation or the
spread of the data? ( range, mean absolute
deviation, quartiles)
 How is data displayed using a histogram, a
dot plot or a box plot?
Common Core Standards and Indicators Assessed
6.SP.1
Recognize a statistical question as one that anticipates variability in the data related to
the question and accounts for it in the answer.
6.SP.2
Understand that a set of data collected to answer a statistical question has a distribution
which can be described by its center, spread and overall shape.
6.SP.3. Recognize that a measure of center for a numerical data set summarizes all of its values
with a single number, while a measure of variation describes how its values vary with a
single number.
6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box
plots.
6.SP.5. Summarize numerical data sets in relation to their context, such as by:
6.SP.5a. Reporting the number of observations.
6.SP.5b. Describing the nature of the attribute under investigation, including how it was measured
and its units of measurement.
6.SP.5c. Giving quantitative measures of center (median and/or mean) and variability (interquartile
range and/or mean absolute deviation), as well as describing any overall pattern and any
striking deviations from the overall pattern with reference to the context in which the data
were gathered.
6.SP.5d. Relating the choice of measures of center and variability to the shape of the data
distribution and the context in which the data were gathered.
Content
Prior Knowledge:
Graphing coordinates
Add, subtract, multiply, divide
integers and decimals
Arranging numbers according to a
certain order
Skills
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Identify statistical questions
Contrast statistical and non-statistical
questions.
Define a statistical question as a
question that allows for the gathering of
variable data.
Describe a set of data in terms of its
center (mean, median), spread (range,
interquartile range, mean absolute
deviation), and overall shape.
Define measure of center for a data set
as the summary of all its values as one
number.
Define measure of variation for a data
set as how the data varies as one
number.
Display numerical data as plots on a
number line.
Display numerical data as plots in a dot
plot
Display numerical data in a histogram.
Display numerical data in a box plot
(box-and-whisker plot).
Record the number of observations
within a numerical data set.
Describe how a data set was measured
and its units of measurement
Calculate measures of center: median
and/or mean.
Calculate measures of variability:
interquartile range and/or mean
absolute deviation.
Describe any overall patterns or
deviations from the overall pattern in
relation to the context of the data
collection
Compare and contrast the measures of
center to the data distribution in the
context of the data collection.
Compare and contrast the measures of
variability to the data distribution in the
context of the data collection.
Vocabulary/ Key Terms
statistical question non-statistical question variability data Center Mean Median Spread
Range quartile interquartile range mean absolute deviation overall shape measure of
center measure of variation dot plot histogram box plot number line observations data
set units of measurement biased unbiased overall pattern measures of center
measures of variability data distribution context of data collection
ASSESSMENT EVIDENCE
Authentic Performance Task(s):
Alignment to Common Core Standards for
Mathematics:
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Statistical and Non-statistical
Questions ( New York Ready
textbook)
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6.SP.1 Recognize a statistical question as
one that anticipates variability in the data
related to the question and accounts for it in
the answer.
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Ann’s Chickens (From Boces)
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6.SP.5 Summarize numerical data in relation
to their context by giving quantitative
measures of center and variability as well as
overall pattern and deviations from such
pattern.
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Writing Scores of 6th Graders on
Sentence Structure (From Boces)
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6.SP.3
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6.SP.4
Recgnize the difference between
the measure of center and the measure of
variation.
Display numerical data on a number
line, including dot plots, histograms and box
plots.
Math Standards for Practice
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
3. Model with mathematics.
4. Use appropriate tools strategically.
5. Attend to precision.
Formative Assessments:
1. Discussions
2. Reflections at the end of class
3. Homework
Summative Assessments:
1. Quiz (graded)
2. Performance Task
Teaching and Learning Activities:
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5.
Introduce unit vocabulary and integrate vocabulary into unit to learn the words.
Use unit guiding questions
Have students complete performance task for the unit.
Use essential question as a post-assessment.
Administer the unit test.
Resources Needed:
Math Curriculum, Impact Math, Math Review Handbook, NYSR – Grade 6