CHAPTER 2Graphical Descriptions of Data

SECTION 2.1Frequency 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

TWO TYPES OF FREQUENCY DISTRIBUTIONS

Grouped Classes are ranges of possible

values

Ungrouped Each class represents a single

value

STEPS TO CREATE A FREQUENCY DISTRIBUTION

Step 1: Determine the number of classes. Normally between 5 and 20, but the classes will be suggested in this lesson.

Step 2: Choose an appropriate class width. 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 =

Note: Round in increments of 50 for large data values. Used rounded number for smaller data values.

CLASS BOUNDARIES

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:

CLASS MIDPOINTS

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

RELATIVE FREQUENCY

Relative frequency is the percentage of the data that falls in a particular class.

Sample size is the total amount of data values.

CUMULATIVE 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.

PRACTICE PROBLEM

SOLUTION

SECTION 2.2AGraphical Displays of Data: Pie Charts and Bar Graphs

PIE CHART

27%

17%

34%

18%

4%

Expense (in dollars)

Rent Food Car Entertainment Other

PARETO CHART

A bar graph that puts the data in descending order.

SIDE-BY-SIDE BAR GRAPH

Represents two sets of data, with bars next to each other.

STACKED BAR GRAPH

Represents two sets of data by stacking the bars.

SECTION 2.2BGraphical 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.

OGIVE (“OH-JIVE”)

An ogive is a line graph that uses the boundaries and the cumulative frequency of the data.

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