# What is the relationship between frequency and relative

### Statistical Language - Describing Frequencies

In so doing, these tables examine the relationships between the two These two -way tables can show relative frequencies for the whole table, for rows, or for. Relative Frequency. How often something happens divided by all outcomes. Example: Your team has won 9 games from a total of 12 games played. quency, and the relationship between these measures. Students will have the Frequency Table of Student Work Hours w/ Relative Frequency.

The second column shows a tally mark indicating the number of people who chose each steak. The third column indicates the frequency with which each steak was chosen.

The tally mark and the frequency number should always match. To create a relative frequency table, we need to do some dividing. A relative frequency table shows the number of people that chose each steak compared to the number of people that did the tasting. Take a look at this new chart.

To find the relative frequency for each steak choice, we need to take the frequency for each choice and divide that number by We are dividing by 20 here because there was a total number of 20 people who tasted the steaks. By choosing a row method, we are comparing men and women in relation to car type. Do you see how this changes our previous interpretation of the data?

This method takes into account the count of men and women separately, giving us a more realistic view of the relationship between the variables.

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Conditional Relative Frequency for Columns: If the two-way relative frequency is for columns, the entries in each column of the table are divided by the total for that column at the bottom. So, what the heck is this method showing us? Are we back to more women than men choosing the Sports Car? The problem is that a column approach does not address the issue of which car men and women prefer. In the column method, we are comparing an SUV to a sports car in relation to gender.

## Relative Frequency

An appropriate question would be, "Were SUVs or sports cars chosen more often by females? What we have seen, by examining all of these tables, is that different tables answer different types of questions about the data.

If you want to look for a relationship between the categorical variables, you will need to prepare a conditional relative frequency table.

You will then need to decide if a "row" method or a "column" method will address the situation you wish to examine. A variety of questions can be answered by examining a two-way frequency table. Let's look at some possibilities: Two-way frequency table How many people responded to the survey?

### Relative Frequency

Was there a higher percentage of males or females choosing an SUV? Associations Based on Conditional Relative Frequency: An "association" exists between two categorical variables if the row or column conditional relative frequencies are different for the rows or columns of the table.

The bigger the differences in the conditional relative frequencies, the stronger the association between the variables. If the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.

Such variables are said to be independent. In our Sports Car and SUV example abovethe row conditonal relative frequencies showed a good degree of difference.

The statistical information is strong enough to support an "association" between gender and choice of vehicle. For instance, you are conducting a random experiment by drawing colored balls from a bag. You take ten balls out of the bag, and you observe that the red balls came up five times. Another good example is to take samples from a production of computer monitors to see whether they are working properly.

We take 50 random samples of the computer monitors to test and determine the relative frequency of defective ones. While conducting the experiment, we learn that ten of the said computer monitors are defective.

- Frequency & Relative Frequency Tables: Definition & Examples
- Difference Between Frequency and Relative Frequency
- Australian Bureau of Statistics

Again we get the relative frequency by dividing the defective computer monitors over the number of samples we tested; 10 defective computer monitors divided by 50 computer monitors tested. Frequency can easily be determined by conducting a simple experiment and noting how many times the event in question occurs; no calculations are needed.