Unit 2: Exploring Data with Graphs and Numerical Summaries Lesson 2-2b – Graphs for Quantitative Data Probability & Stats Essential Question: How do we best summarize simple sets of quantitative data? Dot Plots & Stem-and-Leafs

Learning Objectives 1. Graphs for quantitative data 2. Constructing and interpreting dot plot 3. Constructing and interpreting stem-leaf 2

Learning Objective 1: Graphs for Quantitative Data Now we will explore how to summarize quantitative data variables graphically. Remember that quantitative data is made up of _____________. Bar graphs and pie charts are best suited for ______________ data, not quantitative, so the following two representations (dot plots and stem-and-leaf graphs) help us better present and analyze numerical data. 3 numbers categorical

Learning Objective 2: Dot Plots Dot Plots are statistical graphs used for a quantitative variable. A dot plot shows a dot for each observation placed above its value on a number line When to use a dot plot: Data is discrete Small data sets are preferable 4 simple summarizing single

Learning Objective 2: Dot Plots To construct a dot plot: 1. Draw a horizontal line 2. Label it with the name of the variable 3. Mark regular values of the variable on it 4. For each observation, place a dot above its value on the number line 5

Learning Objective 2: Practice CREATING A DOT PLOT 6 MiniGolf scores… What range do you expect to see in values? How should we set up the values along the line?

Learning Objective 2: Practice INTERPRETING A DOT PLOT 7 The dot plot shown represents the number of passengers boarding a downtown Phoenix bus at its various stops in a day. a) What is the variable? b) How many stops did the bus make? c) What percent of the time did no one board the bus? d) How many passengers physically rode this particular bus? passengers 32 12/ % 0 x x x x x x 2 = 48

Learning Objective 3: Stem-and-leaf Plots Stem-and-leaf plots are similar to dot plots in that they work well with discrete variables (though continuous variables can be used if rounded). A basic stem-and-leaf display contains… two columns separated by a vertical line. The left column contains the stems and the right column contains the leaves. Things to note: Leaves should be ordered from least to greatest Data can be truncated (rounded and/or shortened) in order to help it all fit 8

Learning Objective 3: Stem-and-leaf plots 1) Separate each observation into a stem (first part of the number) and a leaf (typically the last digit of the number) 2) Write the stems in a vertical column ordered from smallest to largest, including empty stems; draw a vertical line to the right of the stems 3) Write each leaf in the row to the right of its stem 9

Learning Objective 3: Practice CREATING A STEM-AND-LEAF 10 Ages at pizza place… What range do you expect to see in values?

Learning Objective 3: Practice INTERPRETING STEM-AND-LEAF 11 The stem-and-leaf shown recent exam in their Algebra 3-4 class. a) The majority of the class scored a… b) How many students scored above an 85%? c) How many students are represented? d) What is the/are the mode(s) score? e) Add the scores of the students who took the exam late in back-to-back form: 87, 75, 73, 82, 91, 93, 99 B

Learning Objective 3: Practice ROUNDING OR TRUNCATING DATA 12 $98.65, $150.33, $125.94, $132.68, $102.45, $164.23, $128.03, $85.45, $144.05, $ Rounding Truncating/ Trimming Rounded wholes to tens, cut off last 0 Notice how specific values are lost