BackChapter 2: Summarizing Data in Tables and Graphs
Study Guide - Smart Notes
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2.1 Organizing Qualitative Data
2.1.1 Organize Qualitative Data in Tables
Qualitative data, often collected from surveys or experiments, must be organized to be useful. Unorganized data is called raw data. One of the primary ways to organize qualitative data is through frequency distributions.
Frequency Distribution: A table that lists each category of data and the number of occurrences for each category.
Relative Frequency: The proportion (or percent) of observations within a category, calculated as:
Relative Frequency Distribution: A table that lists each category of data with its relative frequency.
Example: A physical therapist records the body part requiring rehabilitation for 30 patients. The data is summarized in the following tables:
Body Part | Frequency | Relative Frequency |
|---|---|---|
Back | 12 | 0.4 |
Wrist | 2 | 0.0667 |
Elbow | 1 | 0.0333 |
Hip | 2 | 0.0667 |
Shoulder | 4 | 0.1333 |
Knee | 5 | 0.1667 |
Hand | 2 | 0.0667 |
Groin | 1 | 0.0333 |
Neck | 1 | 0.0333 |
Total | 30 | 1 |
2.1.2 Construct Bar Graphs
A bar graph visually represents categorical data. Each category is labeled on one axis, and the frequency or relative frequency is shown on the other. Bars are of equal width, and their height represents the value.
Pareto Chart: A bar graph where bars are ordered from highest to lowest frequency or relative frequency.
Side-by-Side Bar Graph: Used to compare two or more data sets, typically using relative frequencies for fair comparison.
Horizontal Bar Graph: Useful when category names are lengthy.
Example: Educational attainment in 1990 and 2017 (in thousands):
Educational Attainment | 1990 | 2017 |
|---|---|---|
Not a high school graduate | 39,344 | 26,582 |
High school diploma | 47,643 | 60,032 |
Some college, no degree | 29,780 | 45,110 |
Associate's degree | 9,792 | 18,761 |
Bachelor's degree | 20,313 | 43,585 |
Graduate or professional degree | 11,478 | 27,181 |
Totals | 158,870 | 221,251 |
Relative frequency bar graphs allow for direct comparison between years.
2.1.3 Construct Pie Charts
A pie chart is a circular graph divided into sectors, each representing a category. The area of each sector is proportional to the frequency or relative frequency of the category.
Example: Educational attainment of U.S. residents (2017):
Educational Attainment | Frequency | Relative Frequency | Degree Measure |
|---|---|---|---|
Not a high school graduate | 26,582 | 0.1201 | 43 |
High school diploma | 60,032 | 0.2713 | 98 |
Some college, no degree | 45,110 | 0.2039 | 73 |
Associate's degree | 18,761 | 0.0848 | 31 |
Bachelor's degree | 43,585 | 0.1971 | 71 |
Graduate or professional degree | 27,181 | 0.1229 | 44 |
2.2 Organizing Quantitative Data: The Popular Displays
2.2.1 Organize Discrete Data in Tables
Quantitative data can be discrete (countable values) or continuous (measurable values). Discrete data with few values can be organized similarly to qualitative data, using frequency and relative frequency tables.
Example: Number of customers arriving at Wendy's in 40 intervals:
Number of Customers | Frequency | Relative Frequency |
|---|---|---|
1 | 1 | 0.025 |
2 | 6 | 0.15 |
3 | 1 | 0.025 |
4 | 4 | 0.1 |
5 | 7 | 0.175 |
6 | 11 | 0.275 |
7 | 5 | 0.125 |
8 | 2 | 0.05 |
9 | 2 | 0.05 |
11 | 1 | 0.025 |
2.2.2 Construct Histograms of Discrete Data
A histogram is a graphical representation of the distribution of numerical data. Each bar represents a class (or value), and the height corresponds to the frequency or relative frequency. Bars touch each other to indicate the data is numerical and ordered.
Example: Histogram of customer arrivals at Wendy's shows the distribution of counts per interval.
Key Terms and Concepts
Raw Data: Unorganized data as originally collected.
Frequency Distribution: Table showing counts for each category or value.
Relative Frequency: Proportion of total observations in each category.
Bar Graph: Visual display of categorical data using bars.
Pareto Chart: Bar graph with bars in descending order.
Pie Chart: Circular graph showing proportions of categories.
Histogram: Bar graph for quantitative data, with touching bars.
Discrete Data: Data that can take only specific values (often counts).
Continuous Data: Data that can take any value within a range.
Additional info: For continuous data, classes (intervals) must be created, and histograms are constructed similarly, but with intervals on the axis instead of single values.
