March 21, 2009, Class Notes

A. Frequency Distributions

Classes or intervals are units used to group data entries.

A frequency distribution table shows the number of data entries—frequency (f)—in each
class.

The class width is the difference between the upper and lower limits of each class. It can be
calculated using the following formula:
____Range______

Number of classes
Range of a data set is the difference between the maximum and minimum data entries in the
set. Range is calculated as: Maximum data entry − Minimum data entry
The class boundary is the half-way point between two classes.


Midpoint = (Lower limit) + (Upper limit)


Cumulative frequency of a class is the sum of the frequencies for that class and all the
previous classes.

Relative frequency is the percentage of the data in a particular class. It can be calculated
using the formula:

Relative frequency =
n
f
where,
f is the class frequency and n is the sample size.

B. Graphs and Displays

A histogram is a bar graph often used to display quantitative data. The horizontal scale
displays the class boundaries or midpoints. The vertical scale indicates the frequencies of each
class. In a histogram, the bars touch each other.

A pie chart is a circular graph divided into sectors that represent qualitative data categories,
such as colors, races, and genders. The area of each sector is proportional to the relative
frequency of each data category.

A scatter plot is a graph that represents the relationship between paired data, where each entry
in a data set corresponds to an entry in the second data set. The pair of data entries is shown as
a point or dot in the coordinate plane.