Chapter 11
Data and Graphs
(part 1)
Day…..
1.
Misleading Graphs
2. Frequency Tables and Tally Charts
3.
Histograms and Line Graphs
4. Stem and Leaf Plot and Dot Plots
5. Pie Chart (circle graph)
Day 1
Vocabulary
• Numerical Data- Information gathered for statistical purposes.
• Frequency Table - Used to show the number of times a value appears within
a given period of time.
• Dot Plot - Used to show the frequency of data on a number line.
• Histogram - Used to show the frequency of data divided into equal intervals.
(i.e. a type of bar graph)
• Line Graph- Used to show changes over time.
• Circle Graph - Used to show part to whole comparisons (i.e. percentages)
• Stem and Leaf Plot - Used to arrange data by place value and ordered least to
greatest.
• Stem - The digits of the greatest place value in a stem and leaf plot.
(example: 14 or 243 or 2,876).
• Leaf - The digits of the least place value in a stem and leaf plot.
(example 14 or 243 or 2,876 )
Vocabulary
• Box Plot - A diagram constructed using five values. Used to display
measures of central tendency.
• Measures of Central Tendency- Numbers used to describe the center of a set of
data. The numbers include the mean, median,
and mode.
• Average/ Mean- The sum of two or more quantities divided by the number of
quantities.
• Median- The middle number in a set of data that has been arranged in numerical
order. If the data set has an even number the median is the mean of
the two middle numbers.
• Mode - The number or items that appear most often in a set of data.
• Range - The difference between the greatest number and the least number
in a set of data.
• Outlier- A value that is much higher or much lower than the other numbers in a
set of data.
I Can….
Identify types of graphs.
•
Types of Graphs
Tally Chart – A table created by placing one tally mark, in the designated column or row, every time
an item / value appears or an event occurs. Used to collect and organize data quickly.
Example:
•
Frequency Table – A table used to display a numerical data set, using columns and rows.
Example:
Histogram- A bar graph created using intervals, instead of categories, to display a data set. Another
difference between a histogram and other bar graphs is, a histogram does not have spaces between the
bars, and other bar graph do. This graph is typically used to display difference/similarities during specific
intervals.
Example:
•
Line Graph – A graph created by plotting correlating data, then connecting the points. Used to show
changes over time; such as time, speed, money, height, etc…
Example:
•
Circle Graph- A graph created using percentages. The circle is divided into sections based on each
category's value in comparison to the total data set. (i.e. part to whole comparisons = fractions= %) .
Types of Graphs
•
Stem and Leaf – A graph used to show the shape and distribution of a data set. This graph
is created using a stem column, in which the greatest place value is listed, and a leaf
column, in which the lowest place value is listed.
Example:
•
Dot Plot- A graph used to display a data set for analysis. This graph is created much like a
bar graph using categories and intervals. However, this graph uses dots to display the
change in data, versus bars.
Example:
•
Picture graph- These graphs come in several forms. They can resemble a dot plot, using
pictures instead of dots. They can also resemble a bar graph using larger pictures for
bigger bars and vice versa.
Example:
I Can….
Identify misleading
features on graphs.
Misleading Graphs
Essential Understandings:
•
In statistics, a misleading graph, also known as a distorted graph, is a graph in which data is
misrepresented. This misrepresentation results in the reader drawing an incorrect conclusion
about the data.
•
Graphs can be misleading by accident, due to poor construction, but often graphs are created to
be misleading on purpose.
•
Advertisers and statisticians often use data to prove a point, and they can easily twist that data in
their favor.
The following things are important to consider, when analyzing a graph:
1. Title : Is it there? Is it biased?
2. Labels: Are both axes labeled? Are all sections of a pie chart labeled with a category and a numerical value or is
there a category key?
3. Source of the data: Is it a bias source? How was the data obtained?
4. Key to a pictograph : Is each picture worth the same value? Are they the same size for the same value?
6. Scale: Does the graph start with zero?
7. Breaks: Is there a break in either axis?
8. Spacing: Are the numbers/categories equally spaced?
9. Intervals: Does the scale go up/down consistently?
Partner Work
Please clear your desk of everything
except for a pencil.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
Bell Work
Justify your Response
Homework Check
Vocabulary
• Numerical Data- Information gathered for statistical purposes.
• Frequency Table - Used to show the number of times a value appears within
a given period of time.
• Dot Plot - Used to show the frequency of data on a number line.
• Histogram - Used to show the frequency of data divided into equal intervals.
(i.e. a type of bar graph)
• Line Graph- Used to show changes over time.
• Circle Graph - Used to show part to whole comparisons (i.e. percentages)
• Stem and Leaf Plot - Used to arrange data by place value and ordered least to
greatest.
• Stem - The digits of the greatest place value in a stem and leaf plot.
(example: 14 or 243 or 2,876).
• Leaf - The digits of the least place value in a stem and leaf plot.
(example 14 or 243 or 2,876 )
Vocabulary
• Box Plot - A diagram constructed using five values. Used to display
measures of central tendency.
• Measures of Central Tendency- Numbers used to describe the center of a set of
data. The numbers include the mean, median,
and mode.
• Average/ Mean- The sum of two or more quantities divided by the number of
quantities.
• Median- The middle number in a set of data that has been arranged in numerical
order. If the data set has an even number the median is the mean of
the two middle numbers.
• Mode - The number or items that appear most often in a set of data.
• Range - The difference between the greatest number and the least number
in a set of data.
• Outlier- A value that is much higher or much lower than the other numbers in a
set of data.
I Can….
Read, create, and
interpret frequency tables
and tally charts
Tally Charts and Frequency Tables
Essential Understandings:
•
Tally charts are used to gather and organize data quickly. They are created by placing one tally
mark in the designated category for each time an item/value appears or event occurs. Groups
of 5 are signified by placing a slanted slash across four tallies in a row.
Example:
•
Frequency tables are used to arrange and display tallied data. The created by using a numerical
value in place of the tallies.
Examples:
Independent Practice
Please clear your desk of everything
except for a pencil.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
Justify Your Response
Homework Check
Vocabulary
• Numerical Data- Information gathered for statistical purposes.
• Frequency Table - Used to show the number of times a value appears within
a given period of time.
• Dot Plot - Used to show the frequency of data on a number line.
• Histogram - Used to show the frequency of data divided into equal intervals.
(i.e. a type of bar graph)
• Line Graph- Used to show changes over time.
• Circle Graph - Used to show part to whole comparisons (i.e. percentages)
• Stem and Leaf Plot - Used to arrange data by place value and ordered least to
greatest.
• Stem - The digits of the greatest place value in a stem and leaf plot.
(example: 14 or 243 or 2,876).
• Leaf - The digits of the least place value in a stem and leaf plot.
(example 14 or 243 or 2,876 )
Vocabulary
• Box Plot - A diagram constructed using five values. Used to display
measures of central tendency.
• Measures of Central Tendency- Numbers used to describe the center of a set of
data. The numbers include the mean, median,
and mode.
• Average/ Mean- The sum of two or more quantities divided by the number of
quantities.
• Median- The middle number in a set of data that has been arranged in numerical
order. If the data set has an even number the median is the mean of
the two middle numbers.
• Mode - The number or items that appear most often in a set of data.
• Range - The difference between the greatest number and the least number
in a set of data.
• Outlier- A value that is much higher or much lower than the other numbers in a
set of data.
I Can….
Read, create, and
interpret histograms.
Histograms
Essential Understanding:
Histograms are a type of bar graph, created to display
comparisons among intervals. They are created using a one
quadrant grid. The x-axis is labeled with an interval (example:
time 2pm-4pm) and the y-axis is labeled with a scale (example:
number of shoppers 5, 10, 15). Bars are drawn to show each
interval’s value. Unlike most bar graphs, there is no space
between the bars of a histogram. Readers use this type of graph
to make comparisons and draw conclusions about a data set.
Example:
I Can….
Read, create, and
interpret line graphs
Line Graphs
Essential Understanding:
• Line graphs are graphs created to show changes over time.
They are created using a one quadrant grid. The y-axis is
labeled with a scale (example: hours 10, 20, 30 or dollars
$8,$16, $24). The x-axis can be labeled with categories,
intervals, or a scale. Points are plotted to illustrate how one
value changes in relationship to the other. Readers use this
graph to draw conclusions and make predictions based on the
rate of change illustrated.
Example:
Try it Out….
Take out your marker boards
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
Bell Work
Justify Your Response
Homework Check
Vocabulary
• Numerical Data- Information gathered for statistical purposes.
• Frequency Table - Used to show the number of times a value appears within
a given period of time.
• Dot Plot - Used to show the frequency of data on a number line.
• Histogram - Used to show the frequency of data divided into equal intervals.
(i.e. a type of bar graph)
• Line Graph- Used to show changes over time.
• Circle Graph - Used to show part to whole comparisons (i.e. percentages)
• Stem and Leaf Plot - Used to arrange data by place value and ordered least to
greatest.
• Stem - The digits of the greatest place value in a stem and leaf plot.
(example: 14 or 243 or 2,876).
• Leaf - The digits of the least place value in a stem and leaf plot.
(example 14 or 243 or 2,876 )
Vocabulary
• Box Plot - A diagram constructed using five values. Used to display
measures of central tendency.
• Measures of Central Tendency- Numbers used to describe the center of a set of
data. The numbers include the mean, median,
and mode.
• Average/ Mean- The sum of two or more quantities divided by the number of
quantities.
• Median- The middle number in a set of data that has been arranged in numerical
order. If the data set has an even number the median is the mean of
the two middle numbers.
• Mode - The number or items that appear most often in a set of data.
• Range - The difference between the greatest number and the least number
in a set of data.
• Outlier- A value that is much higher or much lower than the other numbers in a
set of data.
I Can….
Read, create, and
interpret steam and leaf
and dot plots.
Dot Plot
Essential Understanding:
• A dot plot is not unlike a bar graph, the only
difference being that it graphically displays data using
dots (not bars).
Example:
A survey of "How long does it take you to eat breakfast?" has
these results:
Minutes: 0 1 2 3 4 5 6 7 8 9 10 11 12
People: 6 2 3 5 2 5 0 0 2 3 7 4 1
Stem and Leaf Plot
Essential Understandings:
• A Stem and Leaf Plot is a special table in which each
data value is split into a "stem" (the first digit or digits)
and a "leaf" (usually the last digit).
• For example 32 would be split into "3" (stem) and "2"
(leaf). This graph is used to display the shape and
distribution of a data set.
Example:
The height of apple trees in the park are:
12, 13, 13, 15, 17, 18 22, 26, 26, 35, 40
Partner Work
Please clear your desk of everything
except for a pencil.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Bell Work
Justify Your Response
Homework Check
Quick Quiz
Please clear your desk of
everything except for a pencil
and a calculator.
Vocabulary
• Numerical Data- Information gathered for statistical purposes.
• Frequency Table - Used to show the number of times a value appears within
a given period of time.
• Dot Plot - Used to show the frequency of data on a number line.
• Histogram - Used to show the frequency of data divided into equal intervals.
(i.e. a type of bar graph)
• Line Graph- Used to show changes over time.
• Circle Graph - Used to show part to whole comparisons (i.e. percentages)
• Stem and Leaf Plot - Used to arrange data by place value and ordered least to
greatest.
• Stem - The digits of the greatest place value in a stem and leaf plot.
(example: 14 or 243 or 2,876).
• Leaf - The digits of the least place value in a stem and leaf plot.
(example 14 or 243 or 2,876 )
Vocabulary
• Box Plot - A diagram constructed using five values. Used to display
measures of central tendency.
• Measures of Central Tendency- Numbers used to describe the center of a set of
data. The numbers include the mean, median,
and mode.
• Average/ Mean- The sum of two or more quantities divided by the number of
quantities.
• Median- The middle number in a set of data that has been arranged in numerical
order. If the data set has an even number the median is the mean of
the two middle numbers.
• Mode - The number or items that appear most often in a set of data.
• Range - The difference between the greatest number and the least number
in a set of data.
• Outlier- A value that is much higher or much lower than the other numbers in a
set of data.
I Can….
Read, create, and
interpret pie charts
Circle Graph
Essential Understandings:
• In a circle graph (or pie chart), each part of the data is
represented by a “slice” of the circle. In a circle graph, the
size of each sector is determined by the fractional value of the
data it represents. Circle graphs illustrate a part to whole
comparison. Percentages and category keys are used to
analyze the given data set. One of the most common uses for
a circle graph is to display poll results and surveys.
Example:
Group Work
Before we begin…….
1. Complete an exit ticket.
2. Pack up everything except for your
pencil and calculator.
3. Sit quietly unit everyone is ready.
Wrap it Up
• Review
• Questions
• Exit Tickets