Chapter 2 Part 1 Qualitative Data Organizing and Summarizing
Chapter 2: Organizing and Summarizing Data
2.1 Organizing Qualitative Data
Learning Objectives
Organize qualitative data in tables
Construct bar graphs
Construct pie charts
Importance of Organizing Data
Data collected from surveys or designed experiments must be managed for analysis.
Unorganized data is known as raw data.
Objective 1: Organize Qualitative Data in Tables
Frequency Distribution: Lists each data category alongside its occurrence count.
Example: Organizing Qualitative Data into a Frequency Distribution
A physical therapist collects a random sample of 30 patients to analyze rehabilitation needs based on the body parts affected.
Table 1: Records occurrences for each body part requiring rehabilitation.
As reflected in Table 2, the back (12 occurrences) is the most common body part needing rehabilitation.
Relative Frequency Distribution
Relative Frequency: The proportion of observations within each category derived from the formula.
A relative frequency distribution provides category frequencies along with their relative proportions.
For instance, back injury relative frequency calculated as 12/30 = 0.4, indicating it's the most common.
Objective 2: Construct Bar Graphs
A bar graph visually represents data with categories on one axis and their frequencies on the other.
Rectangles are drawn to represent each category’s frequency or relative frequency.
Example: Constructing Frequency and Relative Frequency Bar Graphs
Use Table 3 data to create corresponding bar graphs.
Ensure integrity in representation; avoid charts that start at a non-zero value or have misleading widths/colors.
Pareto Charts
A Pareto chart displays bars in decreasing order of frequency, effectively highlighting categories by their significance.
Side-by-Side Bar Graphs
For comparative analysis (e.g., college completion rates over years), use side-by-side bar graphs to examine different populations using relative frequencies for accuracy.
Example: Comparing Two Data Sets
Tables 4 and 5 compare educational attainment in 1990 vs. 2021.
Key trends reveal an increase in education levels among adults compared to previous years.
The side-by-side graph shows shifts in relative proportions of educational categories.
Horizontal Bar Graphs
Horizontal bars can be beneficial for lengthy category names for better visibility.
Objective 3: Construct Pie Charts
A pie chart displays categories as sectors, with the area proportional to their frequency.
Example: Constructing a Pie Chart
Use Table 6 data (educational attainment in 2021) for pie chart visualization.
Each sector's area correlates to the given frequency for clarity.
Example Breakdown of Pie Chart Data
For the category "not a high school graduate" with a proportion of 0.0893, this equates to approximately 8.93% of the pie chart (32 degrees in total).
Educational Attainment Distribution in 2021
Data representation includes various educational stages:
Not a High School Graduate or Professional Degree: 14%
High School Diploma: 28%
Some College, No Degree: 15%
Associate's Degree: 10%
Bachelor's Degree: 24%
Graduate: 9%
Chapter 2: Organizing and Summarizing Data
2.1 Organizing Qualitative Data
Learning Objectives
Organize qualitative data in tables
Construct bar graphs
Construct pie charts
Importance of Organizing Data
Data collected from surveys or designed experiments must be managed for analysis. Unorganized data is known as raw data.
Objective 1: Organize Qualitative Data in Tables
Frequency Distribution: Lists each data category alongside its occurrence count.
Example: Organizing Qualitative Data into a Frequency Distribution A physical therapist collects a random sample of 30 patients to analyze rehabilitation needs based on the body parts affected.Table 1: Records occurrences for each body part requiring rehabilitation.
Body Part | Occurrences |
|---|---|
Back | 12 |
Knee | 8 |
Shoulder | 5 |
Elbow | 3 |
Ankle | 2 |
As reflected in Table 2, the back (12 occurrences) is the most common body part needing rehabilitation.
Relative Frequency DistributionRelative Frequency: The proportion of observations within each category derived from the formula. A relative frequency distribution provides category frequencies along with their relative proportions.
For instance, back injury relative frequency calculated as 12/30 = 0.4, indicating it's the most common.
Objective 2: Construct Bar Graphs
A bar graph visually represents data with categories on one axis and their frequencies on the other. Rectangles are drawn to represent each category’s frequency or relative frequency.
Example: Constructing Frequency and Relative Frequency Bar Graphs
Bar Graph Example: (Visual representation of the frequency distribution shown above, bars for each body part)
Pareto ChartsA Pareto chart displays bars in decreasing order of frequency, effectively highlighting categories by their significance.
Side-by-Side Bar GraphsFor comparative analysis (e.g., college completion rates over years), use side-by-side bar graphs to examine different populations using relative frequencies for accuracy.
Example: Comparing Two Data Sets
Side-by-Side Bar Graph Example: (Visual representation of educational attainment in 1990 vs. 2021)
Horizontal Bar GraphsHorizontal bars can be beneficial for lengthy category names for better visibility.
Objective 3: Construct Pie Charts
A pie chart displays categories as sectors, with the area proportional to their frequency.
Example: Constructing a Pie Chart
Pie Chart Example: (Visual representation of educational attainment distribution in 2021)
Example Breakdown of Pie Chart DataFor the category "not a high school graduate" with a proportion of 0.0893, this equates to approximately 8.93% of the pie chart (32 degrees in total).
Educational Attainment Distribution in 2021Data representation includes various educational stages:
Not a High School Graduate or Professional Degree: 14%
High School Diploma: 28%
Some College, No Degree: 15%
Associate's Degree: 10%
Bachelor's Degree: 24%
Graduate: 9%