Page 277 - ABCTE Study Guide_Neat

Statistics, Data Analysis, Probability, and Math Reasoning

Frequency Tables and Histograms

Lesson Objective

In this section, we’ll look at a variety of ways to represent data. You’ll see that some data can be
represented in more than one way and will study how these different methods are put to use.

In statistics, there are many ways to analyze and display data. One of the most important features of data
display is the assurance that the audience will understand the data and their implications. To review some
of the methods we use to display data in figures, we will start with some of the basics.

Line Graphs

Line graphs are used to display two-variable data that change continuously over time. Line graphs are
good for showing trends in data. That is, they clearly show how one variable is affected as the other
increases or decreases. They're also good for making predictions of values outside the data set.

Bar Graphs

Bar graphs are used to compare discrete (not continuous) quantities in different categories. The height
of bars in a vertical bar graph and the length of bars in a horizontal bar graph are proportional to the
numbers they represent. Bar graphs are quite useful for displaying results to a survey, in particular.

Stem-and-Leaf Plots

A stem-and-leaf plot organizes data to show its shape and distribution.

Frequency Tables and Histograms

Frequencies tables and histograms are given together because, like line and bar graphs, a histogram is
easier to create if a table of the data is constructed first. In addition, a stem-and-leaf plot looks a bit like a
histogram turned on its side. You’ll see.

A frequency table is a chart that shows the number of times that values within each interval of a data set
occur. Ahistogram is a bar-graph representation of the data in a frequency table that shows the
proportion of data that fall into categories. The categories are nonoverlapping intervals of the data
distribution.

These representations are best demonstrated with an example. Let’s look at the ages of the members of a
small golf club.

Here’s the ordered set:

{42, 43, 43, 44, 46, 47, 47, 47, 48, 48, 48, 52, 52, 53, 54, 54, 54, 55, 56, 57, 57, 57, 57, 59, 60, 61,
62, 63, 64, 66, 66, 68, 69, 70, 71}