ap stats study guides

⚖️  Unit 6 - Inference for Categorical Data: Proportions

😼  Unit 7 - Inference for Qualitative Data: Means

✳️  Unit 8 Inference for Categorical Data: Chi-Square

📈  Unit 9 - Inference for Quantitative Data: Slopes

🧐  Multiple Choice Questions (MCQs)

1.3 Representing a Categorical Variable with Tables




⏱️  2 min read

written by

lusine ghazaryan

Representing Data with Charts

Data can be enormous and hard to understand. For this purpose,  statistics was created to help us organize and analyze data. The first values are organized in the tables. Then data are graphed in different displays. Tables are a necessary step to start analyzing data, but it may fail to highlight essential features with data. The graphical displays are visually attractive, easy to read, and see important patterns of the distribution. For categorical variables, the choices are limited. Bar graphs and Pie charts are the most common displays. 

Frequency Table

Frequency distribution table or relative frequency table for qualitative data lists all categories in one column and the number of elements that belong to each of the categories on the next column. Tally can be used to number the raw data. The frequency table has the following look. 


Source:  Prem S. Mann. Introductory Statistics. John Wiley and Sons Inc. 2010

The variable is stress on job, which assumes three categories; very, somewhat, and none. Since there is some order, stress on job can be ranked as an ordinal variable. The frequency table always reports the sum of the frequencies that makes up our sample.

The frequency table can be extended by adding the relative frequencies and percentages. The relative frequency is found by dividing the frequency for each category by the sum of all frequencies. The percentage is obtained by multiplying the relative frequency of category by 100.   The sum of the relative frequencies should be 1.00 or close to 1.00 if the relative frequencies have been rounded. Similarly, the sum of the percentages is always 100 or close 100 if the percentages have been rounded as well.

Relative frequency of a category = Frequency of that cat category / Sum of all frequencies Percentage = Relative frequency * 100

Based on the relative frequency and percentage distributions of stress on job, we can state that the 33.3% of the employees answered that their jobs are very stressful. Or we can combine the two groups very and somewhat and report that 80 % of the employees  answered that jobs are very or somewhat stressful.

🎥Watch: AP Stats - Analyzing Categorical Variables

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