© 2010 Pearson Education, Inc. All rights reserved Data Analysis/Statistics: An Introduction Chapter 10

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide NCTM Standard: Data Analysis  formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them;  select and use appropriate statistical methods to analyze data;  develop and evaluate inferences and predictions that are based on data.... (p. 48) Instructional programs from prekindergarten through grade 12 should enable all students to

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Students need to know about data analysis and related aspects of probability in order to reason statistically—skills necessary to becoming informed citizens and intelligent consumers. (p. 48) NCTM Standard: Data Analysis

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Definitions Data analysis usually refers to a more informal approach to statistics. It is a relatively new term in mathematics. Statistics once referred to numerical information about state or political territories; it comes from the Latin statisticus, meaning “of the state.” Today, much of statistics involves making sense of data.

Slide Copyright © 2010 Pearson Addison-Wesley. All rights reserved Displaying Data: Part II  Line Graphs  Scatterplots  Choosing a Data Display

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide A line graph typically shows trends in a variable over time. Line Graphs 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.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Line Graphs This is the first example of a depiction of continuous data. All other data examined thus far have been discrete data.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Scatterplots Sometimes a relationship between variables cannot be easily depicted by even a broken line, so a scatterplot may be used.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 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.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 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.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 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: Positive Association

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 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: Negative Association

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 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. Scatterplots: No Association

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Broken Line Graphs Broken line graphs may be used together to demonstrate different sets of data where comparisons may be made.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Broken Line Graphs This graph shows the “crowdedness” of housing from 1940 to 2000, with one broken line showing “crowded” with more than 1 person per room and the other showing “severely crowded” with more than 1.5 persons per room.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 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; order of the data does not matter except for convenience.  Histogram – Used to compare numbers of data items grouped in numerical intervals; order matters.  Box plot – Used to show median, quartile, and extremes of data set. (Section 10-3) Choosing a Data Display

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide  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 sets of data.  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. Choosing a Data Display