Chapter TwoOrganizing and Summarizing

Data

2.1

Organizing Qualitative Data

When data is collected from a survey or designed experiment, they must be organized into a manageable form. Data that is not organized is referred to as raw data. Ways to Organize Data

• Tables

• Graphs

• Numerical Summaries (Chapter 3)

A frequency distribution lists the number of occurrences for each category of data.

EXAMPLE Organizing Qualitative Data into a Frequency Distribution

The data on the next slide represent the color of M&Ms in a bag of plain M&Ms.

Construct a frequency distribution of the color of plain M&Ms.

Yellow Orange Brown Green Green

Blue Brown Red Brown Brown

Orange Brown Red Brown Red

Green Brown Red Green Yellow

Yellow Red Red Brown Orange

Yellow Orange Red Orange Blue

Brown Red Yellow Brown Red

Brown Yellow Yellow Blue Yellow

Yellow Brown Yellow Green Orange

Frequency table

The relative frequency is the proportion or percent of observations within a category and is found using the formula:

A relative frequency distribution lists the relative frequency of each category of data.

frequencyrelative frequency

sum of all frequencies

EXAMPLE Constructing a Relative Frequency Distribution of Qualitative Data

Construct a relative frequency distribution for the M&M data provided earlier.

A bar graph is constructed by labeling each category of data on a horizontal axis and the frequency or relative frequency of the category on the vertical axis. A rectangle of equal width is drawn for each category whose height is equal to the category's frequency or relative frequency.

EXAMPLE Constructing a Frequency and Relative Frequency Bar Graph

Use the M&M data to construct

(a) a frequency bar graph and

(b) a relative frequency bar graph.

A Pareto chart is a bar graph where the bars are drawn in decreasing order of frequency or relative frequency.

Pareto Chart

EXAMPLE Comparing Two Data Sets

The following data represent the consumption of energy (in quadrillion British thermal units) for the years 1980 and 1999.

(a) Draw a side-by-side relative frequency bar graph of the data. (b) Is the make-up of energy consumption changing?

Total Consumption in 1980: 75.98 quadrillion Btu

Total Consumption in 1999: 92.99 quadrillion Btu

(a)

(b) Consumption of petroleum and natural gas has risen from 1980 to 1999, but they represent of lower percentage of total consumption.

A pie chart is a circle divided into sectors. Each sector represents a category of data. The area of each sector is proportional to the frequency of the category.

EXAMPLE Constructing a Pie Chart

The following data represent the consumption of energy (in quadrillion Btus) in 1999. Construct a pie chart of the data.

The degree measure of each sector of the pie is found by multiplying the relative frequency by 360 degrees. For example, the sector corresponding to “Petroleum” has a degree measure of 360(*0.4055) = 145 degrees.