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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