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Math Alliance Project4th Stat Session
Analyzing Quantitative Data
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Review
GAISE Statistical problem solving steps:1. formulate a statistical question2. design and implement a plan to collect data3.analyze the data4.interpret the results in the context of the
original question
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Types of Data
CategoricalGraphs
Bar GraphsPie Chart
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Types of Data
QuantitativeGraphs
Dot plotStemplotHistogramBoxplot
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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)
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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
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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.
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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.
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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
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Activity
Statistical Question: How long are the names of students in our class?
Criteria:PopulationMeasurementVariability
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GAISE Step 2: collect the data
Complete table
Last Name Length
First Name Length Combined length
Hopfensperger 13 Patrick 7 20
Winn 4 Judy 4 8
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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 – lengthsRead down list and place a (•) or (x) for each length above the appropriate mark
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Frequency Table Combined Name – Length Frequency
7 3
8 1
9 0
10 6
11
12
13
14
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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?
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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.
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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?
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Cumulative Frequency tableLength Frequency Cumulative Frequency
7 3 3
8 1 4
9 0 4
10 6 10
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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
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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?
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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
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Mound, normal, bell-shaped
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Symmetric, Uniform
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Skewed
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Bi-Modal
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Stemplot
Example of a stem plotTravel TimesHow many minutes did it take you to get to Gaeslen from your school?Statistical Question?
Burger King Data
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Other examples of stemplots
Students and Basketball players Heights (Navigating book p. 88)
Skateboard prices (p. 23 Data Distributions)
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Activity: How long is a minute?
How good are you at estimating how long a minute is?
Partner one: Head down and hand upLeave hand up until you think one minute has passed
Partner two:Carefully time and recorded how long your partner kept their hand up
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Minute Activity
Switch rolesPartner 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
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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.
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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.
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How is a Histogram Made?
Consider the set of values:3, 11, 12, 19, 22, 23, 24, 25, 27, 29, 35, 36, 37,
45, 49Construct 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
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ReflectionWhy are there no gaps between the
bars in a histogram?
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Histogram Examples
Burger King Data
Migraines Data p. 94NCTM Navigating through Data Analysis in Grades 6-8
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Summary
When would each of these be most useful? What are the advantages and disadvantages of
each type of display?Dotplot
Stemplot
Histogram
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Summary
Purpose is to get a visual display of your data and begin to draw some conclusions about the statistical question.
Describe the shapeEstimate center and spread