Statistics-Target+B-Summarize+Your+Data-Guided+Learning

Statistics-Target B: Summarize Categorical data from a two way frequency table (include joint, marginal, and conditional relative frequencies)
Two Way Frequency Table: A table used to compare different categories of data. The table below was created from a survey where 50 students were asked what foreign language they were taking. In the table below, the different categories being compared are gender (boys and girls), and subject taken (spanish, french, and german). The table can provide different pieces of information. For example, if you wanted to know how many girls are currently taking French, you would look at the "girls" row and move to the "French" column. You can see that it is 12. If you wanted to know the number of total boys who are taking a foreign language, you would look at the "boys" row, and go to the "total" column to find out that 20 boys are taking a foreign language.

Looking at the number of girls taking French is called a joint frequency, because because you are combining 2 different categories (gender and foreign language). Looking at the total number of boys taking a foreign language in general is called a marginal frequency because you are only looking at 1 category (gender).

The marginal frequency (the number of times a certain response is given) is shown in red. The joint frequency (the number of times a certain response is given by a certain group) is shown in blue.

We can interpret the data even further by creating what is called a **two-way conditional relative frequency table**. In this type of table, the percent of a joint frequency or marginal frequency is compared to a total. A two-way conditional relative frequency table can be created with respect to the table total, the table rows, or the table columns.

When a two-way conditional relative frequency table is created with respect to the table total, all of the entries in the table are divided by the overall table total. The entries are then replaced with the decimal which represents the percentage.

When a two-way conditional relative frequency table is created with respect to the rows, the data entries in each row are divided by the total for that row. For example, in order to create the relative frequency for the Boys row, take each entry in that row (10, 2, 8, and 20), and divide by the total for the Boys row (20). This is where the 0.5, 0.1, 0.4, and 1.00 comes from in the table on the right.

When a two-way relative conditional frequency table is created with respect to the columns, the data entries in each column are divided by the total for that column. For example, in order to create the relative frequency for the Spanish column, take each entry in that column (10, 15, and 25), and divide by the total for the Spanish column (25). This is where the 0.4, 0.6, and 1.00 comes from in the table on the right.

**Statistics-Target B-Summarize Your Data-Quick Check:** Create a two-way frequency table and answer the questions that follow. Twenty five kids were asked what they like to do on a hot day. Ten of the 13 girls said they like to go to the pool. Eight of the boys said they like to play video games indoors. Create the two-way frequency table. Then create a two-way conditional relative frequency table with respect to the table total. a) How many boys prefer to go to the pool?

b) What percentage of girls out of all the kids prefer to watch video games?

c) What percentage of the kids are boys?

Statistics-Target B-Summarize Your Data-Quick Check Solutions