Math Alliance Project
4th Stat Session
Analyzing Quantitative Data
Review
GAISE Statistical problem solving steps:
1. formulate a statistical question
2. design and implement a plan to collect data
3. analyze the data
4. interpret the results in the context of the
original question
Types of Data
Categorical
Graphs
Bar Graphs
Pie Chart
Types of Data
Quantitative
Graphs
Dot plot
Stemplot
Histogram
Boxplot
Essential Understanding
• Big Idea 1: The common thread in the statistical
problem solving process is the focus on recognizing,
summarizing and understanding variability in data.
The distribution describes the variability in data.
• There are various ways to represent and summarize a
distribution. These include tables, graphs, and
numerical summaries.
– Representations for the distribution of data on a single
categorical variable include:
• Frequency / relative frequency table
• Frequency / relative frequency bar graph
• Pie chart (circle graph)
Essential Understanding
– Representations for the distribution of data on a single numerical
variable include:
•
•
•
•
•
•
Dot plot
Frequency / relative frequency table
Cumulative Frequency / relative frequency table
Stem and leaf plot
Histogram
Box plot
– With numerical data, identify patterns in the variability and describe
important features of the distribution including:
• Shape of the distribution
– Mound, symmetric, skewed, bi-modal
• Center of the distribution
– Mean, Median, mode
• Spread of the distribution
– Range, interquartile range, mean absolute deviation, standard deviation
Grade 6 Statistics & Probability
Develop understanding of statistical
variability.
•
•
•
1. Recognize a statistical question as one that anticipates variability in the
data related to the question and accounts for it in the answers. For example,
“How old am I?” is not a statistical question, but “How old are the students in
my school?” is a statistical question because one anticipates variability in
students’ ages.
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.
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.
Grade 6 Statistics & Probability
Summarize and describe distributions.
4. Display numerical data in plots on a number line, including dot plots, histograms,
and box plots.
5. Summarize numerical data sets in relation to their context, such as by:
• Reporting the number of observations.
• Describing the nature of the attribute under investigation, including how it was
measured and its units of measurement.
• 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.
• 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.
Essential Understanding
Representations for the distribution of data on a
single numerical variable include:
• Dot plot
• Frequency / relative frequency table
• Cumulative Frequency / relative frequency table
Activity
Statistical Question:
How long are the names of students in our
class?
Criteria:
Population
Measurement
Variability
GAISE Step 2: collect the data
Complete table
Last Name
Leng
th
First Name Length
Combined
length
Hopfensperger
13
Patrick
7
20
Winn
4
Judy
4
8
Gaise Step 3: Analyze the Data
Dotplot (also called a lineplot)
Steps to construct a dotplot:
Horizontal axis scaled to cover the range of
the different name – lengths
Read down list and place a (•) or (x) for each
length above the appropriate mark
Frequency Table
Combined Name – Length
Frequency
7
3
8
1
9
0
10
6
11
12
13
14
Reflection
What are the advantages and disadvantages of
each type of display? (Dotplot vs. Frequency
table)
Does one have to be constructed first in order to
construct the other?
Gaise Step 4: Interpret the results
Original question: How long are the names of
students in our class?
Write an answer to this question using the
dotplot and frequency table to support your
findings.
Extension
Have you ever completed a form that does not
have enough blanks for your entire name?
Suppose a form has only 15 blanks for the
combined name (first, space, last).
How many people in class would be able to
enter their entire name?
Cumulative Frequency table
Length
Frequency
Cumulative Frequency
7
3
3
8
1
4
9
0
4
10
6
10
Relative Cumulative Frequency table
Length
Frequency
Cumulative
Frequency
Relative
Cumulative
Frequency
7
3
3
.3
8
1
4
.4
9
0
4
.4
10
6
10
1.00
Total
10
Interpret the results
If we wanted to design a form so that “most” of
the students in class would have enough room
to write their full name, how long should the
form be?
Essential Understanding
– With numerical data, identify patterns in the
variability and describe important features of the
distribution including:
• Shape of the distribution
– Mound, symmetric, skewed, bi-modal
Mound, normal, bell-shaped
Symmetric, Uniform
Skewed
Bi-Modal
Stemplot
Example of a stem plot
Travel Times
How many minutes did it take you to get to
Gaeslen from your school?
Statistical Question?
Burger King Data
Other examples of stemplots
Students and Basketball players Heights
(Navigating book p. 88)
Skateboard prices (p. 23 Data Distributions)
Activity: How long is a minute?
How good are you at estimating how long a minute
is?
Partner one:
Head down and hand up
Leave hand up until you think one minute has
passed
Partner two:
Carefully time and recorded how long your
partner kept their hand up
Minute Activity
Switch roles
Partner two – while timing talk to your
partner about school, sports, news, your
family
Remember to carefully time and record how
long your partner has their hand up
Back-to- Back Stemplot
Compare estimating one minute between the
groups
What is the statistical question we are
attempting to answer?
Construct a back-to-back stemplot to help
answer our question.
Histograms
A histogram is a graphical display of a frequency
distribution of quantitative data using bars of
the same width (class interval) and heights
dependent on the frequencies.
How is a Histogram Made?
Consider the set of values:
3, 11, 12, 19, 22, 23, 24, 25, 27, 29, 35, 36, 37,
45, 49
Construct a frequency table – decide class width
Class Width
Tally
Frequency
0-10
|
1
10-20
|||
3
20-30
||||||
6
30-40
||||
4
40-50
||
2
Reflection
Why are there no gaps between the
bars in a histogram?
Histogram Examples
Burger King Data
Migraines Data p. 94
NCTM Navigating through Data Analysis in
Grades 6-8
Summary
When would each of these be most useful?
What are the advantages and disadvantages of
each type of display?
Dotplot
Stemplot
Histogram
Summary
Purpose is to get a visual display of your data
and begin to draw some conclusions about
the statistical question.
Describe the shape
Estimate center and spread