Copyright © 2014 Pearson Education. All rights reserved. 3.2-1 3.2 Picturing Distributions of Data LEARNING GOAL Be able to create and interpret basic

Copyright © 2014 Pearson Education. All rights reserved. 3.2-1

3.2 Picturing Distributions of Data

LEARNING GOAL

Be able to create and interpret basic bar graphs, dotplots, pie charts, histograms, stem-and-leaf plots, line charts, and time-series diagrams.

Copyright © 2014 Pearson Education. All rights reserved. 3.2-2Slide 3.2- 2

DefinitionThe distribution of a variable refers to the way its values are spread over all possible values. We can summarize a distribution in a table or show a distribution visually with a graph.


Bar Graphs, Dotplots, and Pareto Charts

A bar graph is one of the simplest ways to picture a distribution. Bar graphs are commonly used for qualitative data.

Each bar represents the frequency (or relative frequency) of one category: the higher the frequency, the longer the bar. The bars can be either vertical or horizontal.


Important Labels for Graphs (cont.)

Horizontal scale and label: The categories should be clearly indicated along the horizontal axis. (Tick marks may not be necessary for qualitative data, but should be included for quantitative data.) Include a label that describes the variable shown on the horizontal axis.

Legend: If multiple data sets are displayed on a single graph, include a legend or key to identify the individual data sets.


DefinitionsA bar graph consists of bars representing frequencies (or relative frequencies) for particular categories. The bar lengths are proportional to the frequencies.

A dotplot is similar to a bar graph, except each individual data value is represented with a dot.

A Pareto chart is a bar graph with the bars arranged in frequency order. Pareto charts make sense only for data at the nominal level of measurement.


Favorite Sports Sport Number of Students

Baseball 25Basketball 18Gymnastics 14Soccer 28Tennis 12

Example: Use the data below to create a bar graph.


DefinitionA pie chart is a circle divided so that each wedge represents the relative frequency of a particular category. The wedge size is proportional to the relative frequency. The entire pie represents the total relative frequency of 100%.


Blood Type A B O AB

Number of donors

7 5 9 4

The Red Cross Blood Donor Clinic had a very successful morning collecting blood donations. Within 3 hours, people had made donations, and the following is a table showing the blood types of the donations: Construct a pie graph to represent the data.

Example:


Definitions

A histogram is a bar graph showing a distribution for quantitative data (at the interval or ratio level of measurement); the bars have a natural order and the bar widths have specific meaning.

A stem-and-leaf plot (or stemplot) is somewhat like a histogram turned sideways, except in place of bars we see a listing of data.


Line Charts

Definition

A line chart shows a distribution of quantitative data as a series of dots connected by lines. For each dot, the horizontal position is the center of the bin it represents and the vertical position is the frequency value for the bin.


ExampleThe scores for a 12-point quiz are listed below arranged from least to greatest.7,5,8,2,3,7,9,11,12,5,9,3,10,12,11Using intervals of 3 points, create a histogram and line chart for the class.

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Copyright © 2014 Pearson Education. All rights reserved. 3.2-1 3.2 Picturing Distributions of Data LEARNING GOAL Be able to create and interpret basic