Chapter 2: Summarizing Data in Tables and Graphs

Organizing Qualitative Data

Introduction

When data is collected from a survey or experiment, it must be organized to facilitate analysis and interpretation. Unorganized data is referred to as raw data. There are several ways to organize data:

• Tables

• Graphs

• Numerical Summaries (covered in Chapter 3)

Organize Qualitative Data in Tables

Qualitative data can be organized using a frequency distribution, which lists each category of data and the number of occurrences for each category.

• Frequency Distribution: A table that displays the frequency (count) of each category.

• Example: A physical therapist surveys 30 patients to determine the body part requiring rehabilitation. The data collected includes categories such as Back, Hand, Wrist, Groin, Elbow, Shoulder, Hip, Knee, Neck.

Body Part	Tally	Frequency
Back	|||| |||| ||	12
Hand	||	2
Wrist	|	1
Groin	||	2
Elbow	||||	4
Shoulder	|||||	5
Hip	||	2
Knee	|	1
Neck	|	1

Relative Frequency Distribution

The relative frequency is the proportion (or percent) of observations within a category. It is calculated using the formula:

$\text{relative frequency} = \frac{\text{frequency}}{\text{sum of all frequencies}}$

• A relative frequency distribution lists each category of data along with its relative frequency.

• Example: If the frequency of 'Back' is 12 and the total number of observations is 30, then the relative frequency for 'Back' is $\frac{12}{30} = 0.4$ or 40%.

Summary Table: Frequency and Relative Frequency

Body Part	Frequency	Relative Frequency
Back	12	0.40
Hand	2	0.07
Wrist	1	0.03
Groin	2	0.07
Elbow	4	0.13
Shoulder	5	0.17
Hip	2	0.07
Knee	1	0.03
Neck	1	0.03

Key Terms

• Qualitative Data: Data that describes qualities or categories rather than numerical values.

• Frequency Distribution: A summary table showing the number of occurrences for each category.

• Relative Frequency: The proportion or percentage of the total observations in each category.

Applications

• Frequency and relative frequency tables are used to summarize survey results, medical data, and other categorical information.

• These tables help in visualizing the distribution of categories and identifying patterns or trends in the data.

Example Calculation

• If a category has a frequency of 5 and the total number of observations is 30:

• Relative frequency = $\frac{5}{30} = 0.167$ or 16.7%

Additional info: The notes continue with graphical representations such as bar graphs and pie charts, which are standard methods for visualizing qualitative data distributions.