4 min readโขdecember 28, 2022

L

Lusine Ghazaryan

Jed Quiaoit

Data can be enormous and hard to understand when observed in its raw, unprocessed likeness. For this purpose,ย statistics was created to help us organize and analyze data. First, values are organized in tables; then, data are graphed in different displays.

Let's say we just finished sending out a survey to our AP Statistics class on how stressful being a student is as a hypothetical occupation with our categories being "very," "somewhat," and "none" (not stressful at all). We, then, have collected 30 responses. How do we organize these responses and make sense of them? ๐ค

One way to do so is to โpileโ the data by counting the number of data values in each category of interest. From there, we can organize these counts into a frequency table, which records the totals and the category names.

At this point, you might wonder: "Wait, what's a frequency table?"

A** 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. Tallies (e.g., ||||) can be used to number the raw data. The frequency table has the following look:ย

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. ๐งฎ

The concept of frequency tables can be extended using **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. ย

With these quantities in mind, a **relative frequency table **is similar, but it gives the percentages for each category instead of counts. 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. Another way to interpret the data is by combining the groups "very" and "somewhat" stressed and report that 80% of the employeesย answered that jobs are very or somewhat stressful. โ

The image below shows the difference between frequency and relative frequency. Unlike frequencies which typically add up to whatever total count of items/respondents there are, tThe 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.

- A
**frequency table**is a list that shows how often each value occurs in a set of data. It shows the*number of times*(or frequency) that each value appears in the data.

For example, consider the following data set: 2, 3, 3, 5, 5, 5, 7, 7, 9. A frequency table for this data set would look like this:

- A
**relative frequency table**is similar to a frequency table, but it shows the relative frequency of each value in the data set. This means that the frequencies are expressed as a*proportion*of the total number of values in the data set.

For example, the relative frequencies for the data set above would be:

- The sum of the relative frequencies in a relative frequency table is
*always*1.

๐ฅ **Watch: AP Stats - ****Analyzing Categorical Variables**

Browse Study Guides By Unit

๐Unit 1 โ Exploring One-Variable Data

โ๏ธUnit 2 โ Exploring Two-Variable Data

๐Unit 3 โ Collecting Data

๐ฒUnit 4 โ Probability, Random Variables, & Probability Distributions

๐Unit 5 โ Sampling Distributions

โ๏ธUnit 6 โ Proportions

๐ผUnit 7 โ Means

โณ๏ธUnit 8 โ Chi-Squares

๐Unit 9 โ Slopes

โ๏ธFrequently Asked Questions

โ๏ธFree Response Questions (FRQs)

๐Big Reviews: Finals & Exam Prep

ยฉ 2023 Fiveable Inc. All rights reserved.