Describing Data: Frequency Tables, Frequency Distributions, and Graphic Presentation
FREQUENCY TABLE: A grouping of qualitative data into mutually exclusive and collectively exhaustive
classes showing the number of observations in each class.
Mutually exclusive means the data fit in just one class
Collectively exhaustive means there is a class for each value
To construct a frequency table
First sort the data into classes
Count the number in each class and report as the class frequency
Convert each frequency to a relative frequency
Each of the class frequencies is divided by the total number of observations
Shows the fraction of the total number observations in each class
Graphic Presentation of Qualitative Data
BAR CHART A graph that shows the qualitative classes on the horizontal axis and the class frequencies on the
vertical axis. The class frequencies are proportional to the heights of the bars.
Use a bar chart when you wish to compare the number of observations for each class of a qualitative variable.
PIE CHART A chart that shows the proportion or percentage that each class represents of the total number of
frequencies.
Use a pie chart when you wish to compare relative differences in the percentage of observations for each class
of a qualitative variable.
Constructing Frequency Distributions
FREQUENCY DISTRIBUTION A grouping of quantitative data into mutually exclusive and collectively
exhaustive classes showing the number of observations in each class.
This is a four-step process
1.Decide on the number of classes 2. Determine the class interval
3.Set the individual class limits 4. Determine the number of the observations in each class
Step 1 Decide on the number of classes
Use the 2k > n rule, where n=180
k is the number of classes n is the number of values in the data set
2k> 180, let k = 8 Souse 8 classes
Step 2 Determine the class interval, i
Round up to some convenient number
Sodecide to use an interval of $400
The interval is also referred to as the class width
Step 3 Set the individual class limits
Lower limits should be rounded to an easy-to-read number when possible
Step 4 Determine the number of observations in each class
The number of observations is the class frequency
Relative Frequency Distributions
To find the relative frequencies, simply take the class frequency and divide by the total number of
observations
Graphic Presentation of a Frequency Distribution
HISTOGRAMA graph in which the classes are marked on the horizontal axis and the class frequencies on the
vertical axis. The class frequencies are represented by the heights of the bars, and the bars are drawn adjacent to
each other.
A histogram shows the shape of a distribution
Each class is depicted as a rectangle, with the height of the bar representing the number in each class
A frequency polygon, similar toa histogram, also shows the shape of a distribution
These are good to use when comparing two or more distributions
Cumulative Frequency Distributions
To construct a cumulative frequency distribution, add each frequency to the frequencies before it
This shows how many values have accumulated as you move from one class down to the next class
Cumulative Relative Frequency Distribution
To construct a cumulative relative frequency distribution, we divide the cumulative frequencies by the total
number of observations
Cumulative Frequency Polygon
Chapter 2 Practice Problems
Question 1
Wellstone Inc. produces and markets replacement covers for cell phones in five different colors: bright white,
metallic black, magnetic lime, tangerine orange, and fusion red. To estimate the demand for each color, the
company set up a kiosk for several hours in the Mall of America and asked randomly selected people which
cover color was their favorite.
a. What is the table called?
b. Draw a bar chart for the table.
c. Draw a pie chart.
d. If Wellstone Inc. plans to produce one million cell phone covers, how many of each color should it produce?
Question 2
Wachesaw Manufacturing Inc. produced the following number of units in the last 16 days.
The information is to be organized into a frequency distribution.
a. How many classes would you recommend?
b. What class interval would you suggest?
c. What lower limit would you recommend for the first class?
d. Organize the information into a frequency distribution and determine the relative frequency distribution.
e. Comment on the shape of the distribution.
Question 3
The following frequency distribution reports the number of frequent flier miles, reported in thousands, for
employees of Brumley Statistical Consulting Inc. during the most recent quarter.
a. How many employees were studied?
b. What is the midpoint of the first class? What lower limit would you recommend for the first class?
c. Construct a histogram.
d. A frequency polygon is to be drawn. What are the coordinates of the plot for the first class?
e. Construct a frequency polygon.
f. Interpret the frequent flier miles accumulated using the two charts.
