Statistics

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Statistics Unit 6
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MCC6.SP.1

• Examples
• Statistical questions that anticipate variability
• Statistical questions that do not anticipate
  variability

• Recognize a statistical question as one that
  anticipates variability in the data related to
  the question and accounts for it in the answers.

• Vocabulary Words
• Statistical Question
• Variability

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Statistical Variability
Identify if the statement below is a statistical
question?
What is a statistical question? A question that
generates a variety of answers is called a
statistical question. Depending on the
question, the type of data gathered can be either
categorical or numerical. An example of a
categorical question is What is your favorite
type of pizza? The answers generated by this
question will be categories of pizza types such
as pepperoni, cheese, or sausage. An example
of a numerical question is How many pencils does
each member of our class have in his or her
desk? A variety of numerical answers about the
number of pencils would be given by a typical 6th
grade class.
How old am I?
What is the height of each person in my class?
What are the math test scores of the students in
my class?
How many letters are in my name?
What is my math test score?
How many letters are in the names of each person
in my class?
How many pets are owned by each student in my
grade level?
What is my height?
Examples of Statistical Questions
Non-Examples of Statistical Questions
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MCC6.SP.2

• Examples
• Describe a set of data by its center
• Describe a set of data by its spread
• Describe a set of data by its overall shape

• 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.

• Vocabulary Words
• Center mean, median, mode
• Spread range, mean absolute deviation
• Shape cluster, gap, outlier

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Shape of Data
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Center of Data
Mean, Median, Mode Fifteen students were asked
to rate how much they like Middle school on a
scale from one to ten. Here is the data
collected 1, 10, 9, 6, 5, 10, 9, 8, 3,
3, 8, 9, 7, 4, 5 The first step is to put
your data in ascending order. 1, 3, 3, 4,
5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10
Lets find the Mean average value for the data
1 3 3 4 5 5 6 7 8 8 9 9
9 10 10 15
97 15

6.5
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Center of Data
Mean, Median, Mode Fifteen students were asked
to rate how much they like Middle school on a
scale from one to ten. 1, 3, 3, 4, 5, 5,
6, 7, 8, 8, 9, 9, 9, 10, 10
Lets find the Median the value for which half
the numbers are longer and half the numbers are
smaller.
Lets find the Mode the number that occurs most
often
Mean 6.5 Median 7 Mode 9
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Variability of Data
Mean Absolute Deviation Fifteen students were
asked to rate how much they like Middle school on
a scale from one to ten. 1, 3, 3, 4, 5, 5,
6, 7, 8, 8, 9, 9, 9, 10, 10
Range Fifteen students were asked to rate how
much they like Middle school on a scale from one
to ten. 1, 3, 3, 4, 5, 5, 6, 7, 8, 8,
9, 9, 9, 10, 10
MEAN
6.5 1 6.5 3 6.5 3 6.5
4 6.5 5 6.5 5 6.5 6
6.5 7 6.5 8 6.5 8 6.5
9 6.5 9 6.5 9 6.5 10
6.5 10 36.5
Lets find the Range Difference between maximum
and minimum data. 10 1 9 Range 9
36.5 15
2.43
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MCC6.SP.3

• Examples
• How a number that describes the measure of center
  is different from a number that describes the
  measure of variation

• 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.

• Vocabulary Words
• Center
• Variation

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Center Vs Variability

• Center
• Summarizes all the values with a single number
• Median the middle number
• Mean the average number

• Variability
• Describes how all the values vary with a single
  number
• Range shows the greatest amount of variation
  between two data values
• MAD shows the average variation between the data
  values

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MCC6.SP.4

• Display numerical data in plots on a number line,
  including dot plots, histograms, and box plots.

• Examples
• Draw a dot plot
• Draw a histogram
• Draw a box plot

• Vocabulary Words
• Dot plot
• Histogram
• Box Plot

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Box Plot
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Box Plot
How to Create a Box-and-Whisker Plot
1) Write the data in order from least to
greatest. 2) Draw a horizontal number line that
can show the data in equal intervals. 3) Find the
median of the data set and mark it on the number
line. 4) Find the median of the upper half of the
data. This is called the upper quartile (Q3).
Mark it on the number line. 5) Find the median of
the lower half of the data. This is called the
lower quartile (Q1). Mark it on the number
line. 6) Mark the lower extreme (minimum) on the
number line. 7) Mark the upper extreme (maximum)
on the number line. 8) Draw a box between the
lower quartiles and the upper quartile. Draw a
vertical line through the median to split the
box. 9) Draw a whisker from the lower quartile
to the lower extreme. 10) Draw a whisker from
the upper quartile to the upper extreme.
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Dot Plots
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Dot Plots
How to Create a Dot Plot
1) Draw a horizontal number line. 2) Determine
and mark a scale of numbers below the line. Make
sure to include the minimum and maximum values in
the data set and all consecutive number values in
between. Example In the data set, there is a
minimum value of 1 and a maximum value of 5. The
number line must include tick marks for every
number value from 1 through 5. A few numbers
before the minimum and a few numbers after the
maximum can be included. 3) A dot is tallied for
each value above the corresponding number. Keep
the imaginary y-axis as a frequency mark to
ensure that dots are plotted correctly. 4) Put a
title on the graph.
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Histogram
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Histogram
How to Create a Frequecty Chart Histogram
1) Make a frequency table of the data by
selecting a range that will contain all of the
data and then divide it into equal intervals. In
the example above, the range of ages is from 0 to
69 so equal intervals of 10 years were selected.
2) Using graph paper, draw an x-axis where each
box will represent an interval of numbers to
represent the ranges. 3) Draw a y-axis with a
scale of numbers appropriate for the data. Common
scales are multiples of 1, 2, 5, 10 or 20. 4)
Draw each bar on the histogram to correlate the
intervals with the frequency of occurrence. 5)
Title the graph and the x and y-axis.
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MCC6.SP.5

• Summarize numerical data sets in relation to
  their context, such as by

• Examples
• Draw a frequency chart to report the number of
  observations
• Describe a graph or information on how it was
  measured and its unit of measurement

MCC6.SP.5a
Reporting the number of observations.
MCC6.SP.5b
Describing the nature of the attribute under
investigation, including how it was measured and
its units of measurement.

• Vocabulary Words
• Frequency Chart

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Reporting of Observations

• How many families have 3 children?
• 12 families
• How many families have less than 3 children?
• 11 families

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Describing the Units

• What information was collected to create this
  graph?
• 28 families with 1 5 children were surveyed
• Families reported how many children they had
• What are the units of measurement used within
  this graph?
• Number of children in families
• Number of families with specified amount of
  children

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MCC6.SP.5

• Summarize numerical data sets in relation to
  their context, such as by

• Examples
• Describe a box plot in terms of median and
  interquartile range
• Describe a histogram in terms of median, mean,
  and mean absolute deviation
• Describe a dot plot in terms of mean, median, and
  mean absolute deviation

MCC6.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 was
gathered.

• Vocabulary Words
• Outlier

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Measures of Center

•  

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Measures of Variability

•  

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MCC6.SP.5

• Summarize numerical data sets in relation to
  their context, such as by

• Examples
• How does the measure of center relate to the
  shape of the data set?
• How does the measure of variability relate to the
  shape of the data set?

MCC6.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 was gathered.
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Representative Measures of Center
Use the Dot Plot to identify the Mean, Median
Mode
Mean Average 11111111222223334
445 44 44/20 2.2 Mean 2.2
Median Number in middle of set 1,1,1,1,1,1,1,1,
2,2,2,2,2,3,3,3,4,4,4,5 Median 2
Mode Number used most in the
set 1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,5 Mode
1
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Representative Measures of Variability
Use the Dot Plot to identify the Range, IQR, and
MAD
 
IQR 1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,5 1s
t Quartile 1 3rd Quartile 3 IQR 3 1 2
Range 5 1 4
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Math Resource