2-1 Organizing Data

2-1 Organizing Data

You will be able to:

**Organize data using a frequency distribution.

Introduction

• The most convenient method of organizing data is to construct a frequency distribution.

• The most useful method of presenting the data is by constructing statistical charts and graphs. 

Raw Data: data collected in its original form

Quantitative and Qualitative

Frequency Distribution

• Since little information can be obtained from looking at raw data, the researcher organizes the data into what is called a frequency distribution.

• A frequency distribution consists of classes and their corresponding frequencies.

• The frequency of a class then is the number of data values contained in a specific class. A frequency distribution is shown for the preceding data set.

Frequency Distributions:

Quantitative and Qualitative

Grouped Frequency Distributions Steps

• Find the Range = Highest Value-Lowest Value

• Select the number of classes desired (usually between 5 and 20).

• Find the class width:

   $Class\ Width=\frac{Range}{number\ of\ classes}$  

• Round the width UP to the nearest whole number.

• Find the class boundaries by subtracting 0.5 from each lower class limit and adding 0.5 to each upper class limit.

• Tally the data

• Find the numerical frequencies from the tallies.

Example of Grouped Frequency Distribution

Cumulative Frequency Distribution

A cumulative frequency distribution is a distribution that shows the number of data values less than or equal to a specific value (usually an upper boundary)

Ungrouped Frequency Distribution

• Use when the range of the data values is relatively small.

• Construct using single data values for each class. 

Miles per Gallon for SUVs

The data shown here represent the number of miles per gallon (mpg) that 30 selected four-wheel-drive sports utility vehicles obtained in city driving.

Construct a frequency distribution, and analyze the distribution.

Weights of the NBA’s Top 50 Players

Listed are the weights of the NBA’s top 50 players. Construct a grouped frequency distribution and a cumulative frequency distribution with 8 classes. Analyze the results in terms of peaks, extreme values, etc.

 GRE Scores at Top-Ranked Engineering Schools

The average quantitative GRE scores for the top 30 graduate schools of engineering are listed. Construct a grouped frequency distribution and a cumulative frequency distribution with 5 classes.