10 Chapter Data Analysis/Statistics: An Introduction Copyright © 2016, 2013, and 2010, Pearson Education, Inc.

10-3 Displaying Data: Part II Students will be able to understand and explain: • Line graphs; • Scatter plots for two variables; • Relationship between a pair of variables using a scatterplot; • Trend lines; • Positive association, negative association, and no association; and • How to choose a data display.

Line Graphs A line graph typically shows trends in a variable over time. Time is usually marked on the horizontal axis, with the variable being considered marked on the vertical axis. Consecutive data points are connected by line segments.

Line Graphs This is the first example of a depiction of continuous data. All other data examined thus far have been discrete data.

Scatterplots Sometimes a relationship between variables cannot be easily depicted by even a broken line, so a scatterplot may be used.

Scatterplots This scatterplot shows the relation between the number of hours studied and quiz scores. The highest score is a 10 and the lowest is 1.

Scatterplots Now a trend line has been added to the figure. A trend line is a line that closely fits the data and can be used to describe it. A trend line can be used to make predictions.

Scatterplots: Positive Association If the trend line slopes up from left to right, there is a positive association between the data on the horizontal axis and the data on the vertical axis. An increase in the value of the variable on the horizontal axis would predict an increase in the value of the variable on the vertical axis.

Scatterplots: Negative Association If the trend line slopes down from left to right, there is a negative association between the data on the horizontal axis and the data on the vertical axis. An increase in the value of the variable on the horizontal axis would predict a decrease in the value of the variable on the vertical axis.

Scatterplots: No Association If the points do not approximately fall about any line, we say there is no association. No prediction of one variable can be made based on the value of the other.

Double Line Graphs Double line graphs may be used together to demonstrate different sets of data where comparisons may be made.

Broken Line Graphs This graph shows the “crowdedness” of housing from 1940 to 2000, with one line showing “crowded” with more than 1 person per room and the other showing “severely crowded” with more than 1.5 persons per room.

Choosing a Data Display Choosing the right display is not always easy, and there may be more than one appropriate choice. Bar graph – Used to compare numbers of data in grouped categories. Histogram – Used to compare numbers of data items typically grouped in numerical intervals; order matters.

Choosing a Data Display Stem and leaf plot – Used to show each value in a data set and to group values into intervals. Scatterplot – Used to show the relationship between two variables. Line graph – Used to show how data values change over time; normally used for continuous data. Circle graph – Used to show the division of a whole into parts.