Chapter 4: Probability & Statistics Section 4.5: Charts & Graphs Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Organizing Data We will examine how to read and create several types of charts and graphs. Stem-and-Leaf Plots: Displays Groups of Numerical Data Bar Graphs: Graphical Representation of Data into Disjointed Bins Histograms: Graphical Representation of Data into Continuous Bins Line Graphs: Graphical Representation of Data Showing Change over Time Pie Charts: Used to Show Relative Proportions of Data in Relation to the Entire Data Set Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Stem-and-Leaf Plots For two-digit numbers, group the data into similar ranges according to the tens digits. That is, group together all the numbers in the 90s, the 80s, 70s, and so on. When putting them into a stem-and-leaf chart, the tens digits are the “stems,” and the ones digit for each number is a “leaf.” Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Stem-and-Leaf Plots Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99 STEM LEAVES 9 8 7 6 5 STEM LEAVES 9 8 7 6 5 STEM LEAVES Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Stem-and-Leaf Plots Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99 STEM LEAVES 9 8 7 6 5 STEM LEAVES 9 8 7 6 5 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Stem-and-Leaf Plots Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99 STEM LEAVES 9 8 7 6 5 STEM LEAVES 9 0 4 8 7 6 5 STEM LEAVES 9 8 7 6 5 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Stem-and-Leaf Plots Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99 STEM LEAVES 9 0 4 9 8 8 7 7 9 7 8 7 6 5 6 7 9 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Stem-and-Leaf Plots Example: Create a stem-and-leaf chart for the following data. 56, 90, 94, 88, 57, 78, 87, 87, 89, 87, 65, 59, 88, 99 STEM LEAVES 9 0 4 9 8 7 7 7 8 8 9 7 6 5 6 7 9 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Bar Graphs Group the data into categories (called bins) - in any order - and list the name of each bin under the horizontal axis. Label the vertical axis with numbers, starting at 0, and equally spacing the intervals, going as high as needed. Create a bar for each distinct bin, with the height of the bar indicating the number of items in the corresponding bin. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Bar Graphs Example: A bag contains 6 red jellybeans (R), 2 green jellybeans (G), 7 yellow jellybeans (Y), and 4 blue jellybeans (B). Create a bar graph that displays this data. 6- 4- 2- R G Y B Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Histograms A histogram is very similar to a bar chart. In a bar chart the bins are separate and distinct, and can be put in any order. In a histogram, the bars represent continuous bins (usually time periods), and must be in order, with no gaps between them. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Histograms Example: The table below represents the number of students taking MATH 104B in five consecutive fall and spring semesters. Create a histogram for the data. Semester Students Fall ‘12 450 Spring ‘13 505 Fall ‘13 420 Spring ‘14 598 Fall ‘14 618 700 - 600 - 500 - 400 - 300 - 200 - 100 - - | | | | | F12 S13 F13 S14 F14 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Line Graphs Line graphs are used to emphasize the change in data over time. Where the focus on a histogram is the height of the individual bars, the focus on a line graph is the slope of the lines between each bin. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Pie Charts Pie charts are a way to represent 100% of a data set, where each disjoint (non-overlapping) group in the set is represented by an appropriately sized sector. The size of the sector is determined by the percent of the group size in the data set. Once we have the percent of the data, we multiply that percent by 360o to get the number of degrees of the sector. Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Pie Charts Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results. There were 40+20+50+90 = 200 voters. Al got 40/200 = 0.2 = 20% of the votes. 20% of 360o = 0.2(360o) = 72o Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Pie Charts Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results. There were 40+20+50+90 = 200 voters. Al got 40/200 = 0.2 = 20% of the votes. 20% of 360o = 0.2(360o) = 72o Beth got 20/200 = 0.1 = 10% of the votes. 10% of 360o = 0.1(360o) = 36o Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Pie Charts Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results. There were 40+20+50+90 = 200 voters. Al got 40/200 = 0.2 = 20% of the votes. 20% of 360o = 0.2(360o) = 72o Beth got 20/200 = 0.1 = 10% of the votes. 10% of 360o = 0.1(360o) = 36o Cindy got 50/200 = 25% of the votes. 25% of 360o = 0.25(360o) = 90o Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Pie Charts Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results. There were 40+20+50+90 = 200 voters. Al got 40/200 = 0.2 = 20% of the votes. 20% of 360o = 0.2(360o) = 72o Beth got 20/200 = 0.1 = 10% of the votes. 10% of 360o = 0.1(360o) = 36o Cindy got 50/200 = 25% of the votes. 25% of 360o = 0.25(360o) = 90o Dave got 90/200 = 45% of the votes. 45% of 360o = 0.45(360o) = 162o Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates
Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Pie Charts Example: In a recent student council election, 40 students voted for Al, 20 voted for Beth, 50 voted for Cindy, and 90 voted for Dave. Create a pie chart that represents these results. There were 40+20+50+90 = 200 voters. Al got 40/200 = 0.2 = 20% of the votes. 20% of 360o = 0.2(360o) = 72o Beth got 20/200 = 0.1 = 10% of the votes. 10% of 360o = 0.1(360o) = 36o Cindy got 50/200 = 25% of the votes. 25% of 360o = 0.25(360o) = 90o Dave got 90/200 = 45% of the votes. 45% of 360o = 0.45(360o) = 162o Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates