CHAPTER 2
Graphical Descriptions of Data
SECTION 2.1
Frequency Distributions

After collecting the data, we need to organize the data. This
chapter will describe different ways to organize the data.
ORDERED ARRAY

Arranging data from least to greatest or vice versa.
VOCABULARY
Grouped

Classes are ranges of possible
values
Ungrouped

Each class represents a single value
TWO TYPES OF FREQUENCY
DISTRIBUTIONS
STEPS TO CREATE A FREQUENCY DISTRIBUTION

Step 1: Determine the number of classes.


Step 2: Choose an appropriate class width.



Normally between 5 and 20, but the classes will be suggested in this lesson.
Find the range, then round up. The class width is the difference between lower
limits.
Step 3: Find the class limits.

The lower limit is the smallest number that can belong to the class.

The upper limit is the largest number that can belong to the class.
Step 4: Determine the frequency of each class.

Make a tally mark for each piece of data in the appropriate class, then count the
tally marks to find the total frequency for each class.
EXAMPLE
Class width =
2499−859
6
= 273.33 = 274. 𝑅𝑜𝑢𝑛𝑑 𝑡𝑜 $300 𝑡𝑜 𝑎𝑝𝑝𝑒𝑎𝑙 𝑡𝑜 𝑎𝑢𝑑𝑖𝑒𝑛𝑐𝑒.
Note: Round in increments of 50 for large data values. Used rounded number for smaller data values.

The class boundaries split the difference in the gap between the
upper limit of one class and the lower limit of the next class.

To find the class boundary, add the upper limit of one class to the
lower limit of the next class and divide by two.

Example:

𝑈𝑝𝑝𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 = 10
𝐿𝑜𝑤𝑒𝑟 𝑙𝑖𝑚𝑖𝑡 = 11
CLASS BOUNDARIES
10+11
2
= 10.5

The class midpoint is the midpoint of the lower limit and the upper
limit.

To find the class midpoint, add the lower and upper limit of the
same class, then divide by 2.

Example:

Lower limit = 800
Upper limit = 1099
CLASS MIDPOINTS
800+1099
2
= 949.5

Relative frequency is the percentage of the data that falls in a
particular class.

Sample size is the total amount of data values.
RELATIVE FREQUENCY

Cumulative frequency is the sum of the frequency for a given
class and the frequencies of all previous classes.

The cumulative frequency of the last class should equal the
sample size.
CUMULATIVE FREQUENCY
PRACTICE PROBLEM
SOLUTION
SECTION 2.2A
Graphical Displays of Data: Pie Charts and Bar Graphs
Expense (in dollars)
4%
18%
27%
17%
34%
PIE CHART
Rent
Food
Car
Entertainment
Other
PARETO CHART

A bar graph that puts the data in descending order.

Represents two sets of data, with bars next to each other.
SIDE-BY-SIDE BAR GRAPH
STACKED BAR GRAPH

Represents two sets of data by stacking the bars.
SECTION 2.2B
Graphical Displays of Data: Histograms, Polygons, and Stem and Leaf Plots
RELATIVE FREQUENCY HISTOGRAM

Similar to the histogram, except the height of the bars is the
relative frequency instead of the frequency.
HOW TO CREATE A FREQUENCY POLYGON

Step 1: Mark the class boundaries on the x-axis and the
frequencies on the y-axis. There will be two extra classes, one on
the lower end and one on the upper end, both with a frequency
of 0.

Step 2: Add the midpoint to the x-axis, then plot a point at the frequency right above
the midpoint.

Step 3: Join each point with a line segment.

An ogive is a line graph that uses the boundaries and the cumulative frequency of
the data.
OGIVE (“OH-JIVE”)
OR
DOT PLOT

Similar to the stem and leaf other than it is a number line with dots representing the
leaves.
SECTION 2.3
Analyzing Graphs

Time-Series Graph – a picture of how data changes over time and has a variable of
time as the horizontal axis.

Cross-Sectional Graph – a picture of the data at a given moment in time. Neither axis will
have a variable of time