Chapter 2
Key Ideas
Frequency Distribution, Relative Frequency Distribution, Cumulative Frequency Distribution, Histogram, Relative Frequency
Histogram, Normal Distribution, Dotplot, Stemplot, Pie Chart, Scatterplot, Time-Series G raph,
Section 2-1: Overview
Once you obtain data from a study, it is often useful to put it into a visual context. This allo ws people to see what is happening in the
dataset instead of seeing a lot of numbers. This chapter deals with a variety of ways to display data to make it easier to understand
what the results are saying.
Section 2-2: Frequency Distributions
Frequency Distributions are tables that display data according to frequencies (or counts) of how many data values fall into particular
intervals, or categories. They are called distributions because they show the way the observations are distributed among the different
groups.
•
A basic frequency distribution lists the data values (groups) along with their corresponding frequencies.
•
A cumulative frequency distribution can be useful for ordered data (e.g. data arranged in intervals, measurement data, etc.).
Instead of reporting frequencies, the recorded values are the sum of all frequencies for values less than and including the
current value.
•
A relative frequency distribution lists the data values along with the percent of all observations belonging to each group.
These relative frequencies are calculated by dividing the frequencies for each group by the total number of observations.
Example: Suppose we take a sample of 200 U.S. households and record the number of people living there. We obtain the following:
Number of
People Frequency Number of
People
Cumulative
Frequency Number of
People
Relative
Frequency
1 10 1 10 1 5%
2 50 2 60 2 25%
3 90 3 150 3 45%
4 40 4 190 4 20%
5 6 5 196 5 3%
6 4 6 200 6 2%
Freq. Distribution Cumulative Freq. Distribution Relative Freq. Distribution
Section 2-3: Histograms
A histogram is a special kind of bar graph that applies to quantitative data (discrete or continuous). The horizontal axis represents the
range of data values. The bar height represents the frequency of data values falling within the interval formed by the width of the bar.
The bars are also pushed together with no spaces between them.
Example: Number of people in 200 U.S. households (see above).
Note: Here the data values only take on integer values, but we still split the range of values
into intervals. In this case, the intervals are [1,2), [2,3), [3,4), etc. Notice that this graph is
also close to being bell-shaped. A symmetric, bell-shaped distribution is called a normal
distribution. These types of distributions will be discussed later.
Also: A relative frequency histogram is the same as a regular histogram, except instead o f
the bar height representing frequency, it now represents the relative frequency (so the y-axis
runs from 0 to 1, which is 0% to 100%).
10/200
50/200
etc.
