Business Statistics Chapter 2 - Descriptive Statistics (Tabular & Graphical Displays)

Frequency Distribution (Categorical Variable)

tabular summary of data showing the number (frequency) of observations in each of several non-overlapping categories or classes.

Relative Frequency

The proportion of the total number of data items belonging to the class

Percent Frequency

The relative frequency multiplied by 100.

Bar chart

a graphical display for depicting categorical data summarized in a frequency, relative frequency or percent frequency distribution.

On one axis (usually the horizontal axis),

we specify the labels used for the classes

(categories).

• A frequency, relative frequency, or percent

frequency scale is used for the other axis

(usually the vertical axis).

• Using a bar of fixed width, drawn above

each class label, we extend the height

appropriately.

• The bars are separated to emphasize the

fact that each class is a separate category.

Pie Chart

provides another graphical display for presenting relative frequency and percent frequency distributions for categorical data

• Use the percent frequencies to subdivide the circle into sectors that are proportional to the precent frequency for each class

• Similar calculations for the other classes yield the __ ____ shown

Steps to Define the classes for a Frequency Dist.

1. Number of classes

2. Width of the classes

Class Limits

Are chosen so that classes do not overlap, and each data item only belongs to one class

Relative Frequency of a Class

We define the _______________ and percent frequency distributions for quantitative data in the same manner as for categorical data.

cumulative frequency distribution

shows the number of items with values less than or equal to the upper limit of each class

cumulative relative frequency distribution

shows the proportion of items with values less than or equal to the upper limit of each class.

cumulative percent frequency distribution

shows the percentage of items with values less than or equal to the upper limit of each class

Dot Plot

• one of the simplest graphical summaries of quantitative data.

• the horizontal axis shows the range for the data, with class limits and each data value is represented by a dot placed above the axis.

• Show the details of the data and are useful for comparing the distribution of the data for two or more variables

Histogram

a common graphical display that can be prepared for quantitative data previously summarized in a frequency, relative frequency, or percent frequency distribution.

• The variable of interest is placed on the horizontal axis.

• A rectangle is drawn above each class interval with its height corresponding to the interval’s frequency, relative frequency, or percent frequency.

• Unlike a bar graph, this has no natural separation between rectangles of adjacent classes

• It gives info about the shape and form of a distribution

Moderately Skewed Left Histogram

Moderately Skewed Right Histogram

Highly Skewed Right

Symmetric Skewed Histogram

Stem-and-Leaf Display

Shows both the rank order and shape of a distribution of data. It is similar to a histogram on its side, but it has the advantage of showing the actual values.

• The leading digits of each data item are arranged to the left of a vertical line.

• To the right of the vertical line, we record the last digit for each item in rank order.

• Each line (row) in the display is referred to as a stem.

• Each digit on a stem is a leaf.

Crosstabulation

a statistical tool in business analytics that analyzes the relationship between two or more categorical variables by arranging them in a matrix format.

• It displays joint frequency distributions to identify patterns, trends, and dependencies between, for example, demographic groups and product preferences.

Scatter Diagram

is a graphical presentation of the relationship between two quantitative variables.

Trendline

Is a line that provides an approximation of the relationship

Positive Relationship Trendline

Negative Relationship Trendline

No Apparent Relationship Trendline

Side-by-Side Bar Chart

is a graphical display for depicting multiple bar charts on the same display.

Stacked Bar Chart

Can also be used to compare 2 varibales on the same display, each bar is broken into rectangular segments of a different color showing the relative frequency of each class in a manner similar to a pie chart.

Data visualization

is the use of graphical displays to summarize and present data.

The goal of __________ is to communicate, as effectively and clearly as possible, the key information about the data.

Guidelines for an effective Graphical Display

• It displays a clear and concise title.

• It keeps the display simple, yet informative.

• Each axis is clearly labeled, and units are provided.

• The two colors used are distinct, and a legend is provided to explain their use.

To Make Comparisons

Side-by-Side Bar Chart: used to compare two variables

Stacked Bar Charts: used to compare the relative frequency or percent frequency of two categorical variables

To Show Relationships

Scatter diagram: used to show the relationship between two quantitative variables

Trendline: used to approximate the relationship of data in a scatter diagram

Data Dashboard

widely used data visualization tool that organizes and presents key performance indicators (KPIs) used to monitor an organization or process.

• provides timely summary information that is easy to read, understand, and interpret.

Guidelines for Data Dashboards

• Minimize the need for screen scrolling.

• Avoid unnecessary use of color or 3D displays.

• Use borders between charts to improve readability.