Chapter 2 Graphs, Charts, and Tables - Describing Your Data ©

Chapter 2 - Chapter Outcomes After studying the material in this chapter, you should: Be able to construct frequency distributions both manually and with your computer. Be able to construct and interpret a histogram. Know how to construct and interpret various types of bar charts. Understand the purpose of a Pareto chart and be able to construct one.

Chapter 2 - Chapter Outcomes (continued) After studying the material in this chapter, you should: Be able to create a line chart and interpret the trend in the data. Be able to construct a scatter plot and interpret it. Be able to develop and interpret joint frequency tables.

Frequency Distributions frequency distribution A frequency distribution is the summary of a set of data that displays the number of observations in each of the distribution’s distinct categories or classes.

Frequency Distribution of Years in College (Figure 2-1)

Frequency Distribution of Years in College (Figure 2-2)

Discrete Data Discrete data Discrete data are data whose possible values are countable.

Relative Frequency relative frequency The relative frequency is the proportion of total observations contained in a given category.

Relative Frequency Distribution of Years in College (Figure 2-3)

Grouping Data Into Classes Continuous data : Data whose possible values are uncountable and which may assume any value in an interval. Data array : Data that have been sorted in ascending or descending order. Mutually exclusive classes : Classes that do not overlap. All inclusive classes : A set of classes that contains all the possible data values. Equal width classes : Distance between lowest possible value and highest possible value in each class is the same for all classes.

Steps for Grouping Data Into Classes Step 1: Determine the number of groups or classes to use. (Generally 5-20 classes.) Step 2: Establish the class width.

Class Width

Steps for Grouping Data Into Classes Step 1: Determine the number of groups or classes to use. Step 2: Establish the class width. Step 3: Determine the class boundaries for each class.

Steps for Grouping Data Into Classes Step 1: Determine the number of groups or classes to use. Step 2: Establish the class width. Step 3: Determine the class boundaries for each class. Step 4: Count the number of values in each class.

Cumulative Frequencies Cumulative frequency distribution : A summary of a set of data that displays the number of observations with values less-than- or-equal-to the upper limit of each of its classes. Cumulative relative frequency distribution : A summary of a set of data that displays the proportion of observations with values less- than-or-equal-to the upper limit of each of its class.

Frequency Histograms (Figure 1-2)

Frequency Histograms A histogram shows three general types of information: It provides visual indication of where the approximate center if the data is. We can gain an understanding of the degree of spread, or variation, in the data. We can observe the shape of the distribution.

Histograms Showing Different Centers

Histograms - Same Center, Different Spread

Joint Frequency Distributions joint frequency distribution A joint frequency distribution is a summary of a bivariate set of data that displays the number of observations that exhibit the respective joint characteristics of one value taken from each of the variables that define the data set.

Bar Charts bar chart A bar chart is a graphical representation of a categorical data set in which a rectangle or bar is drawn over each category or class. The length of each bar represents the frequency or percentage of observations in each category.

Bar Charts (Table 2-6)

Bar Charts (Figure 2-14) Brazil and Mexico provided the most income

Pareto Charts pareto chart A pareto chart is a bar chart that is sorted so that the categories or classes are arranged from the highest to lowest with respect to the magnitude of the displayed variable associated with each category or class.

Pie Charts pie chart A pie chart is a graph in the shape of a circle: The circle is divided into “slices” corresponding to the categories or classes to be displayed. The size of each slice is proportional to the magnitude of the displayed variable associated with each category or class.

Pie Charts

Pie Charts (Figure 2-21)

Line Charts line chart A line chart is a two-dimensional chart showing time on the horizontal axis and the variable of interest on the vertical axis.

Line Charts (Figure 2-23) Increasing Sales Sales Trend

Line Charts (Figure 2-25) Profit and sales going in opposite directions

Scatter Diagrams scatter diagram A scatter diagram is a two-dimensional graph of plotted points in which the vertical axis represents values of one variable and the horizontal axis represents values of the other.

Scatter Diagrams X Y X Y Positive LinearNegative Linear

Scatter Diagrams Dependent and Independent Variables dependent variable A dependent variable is one whose values are thought to be a function of the values of another variable. (y-axis) independent variable An independent variable is one whose values are thought to impact the values of the dependent variable. (x-axis)

Key Terms All-Inclusive Classes Bar Chart Class Boundaries Class Width Continuous Data Cumulative Frequency Cumulative Relative Frequency Data Array Dependent Variable Discrete Data Equal-Width Classes Frequency Distribution Frequency Histogram Independent Variable Joint Frequency Distribution Line Chart

Key Terms (continued) Mutually-Exclusive Classes Pareto Chart Pie Chart Relative Frequency Scatter Diagram