1. Two Way Frequency Tables
Unit 6 Describing data
Two Way Frequency Tables

2. Two-Way Frequency Tables
Standards:
MGSE9-12.S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.  
MGSE9-12.S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  
MGSE9-12.S.ID.6a Decide which type of function is most appropriate by observing graphed data, charted data, or by analysis of context to generate a viable (rough) function of best fit. Use this function to solve problems in context. Emphasize linear, quadratic and exponential models.  
MGSE9-12.S.ID.6c Using given or collected bivariate data, fit a linear function for a scatter plot that suggests a linear association.  

3. Two-way frequency tables
Standards continued:
MGSE9-12.S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.  
MGSE9-12.S.ID.8 Compute (using technology) and interpret the correlation coefficient "r" of a linear fit. (For instance, by looking at a scatterplot, students should be able to tell if the correlation coefficient is positive or negative and give a reasonable estimate of the "r" value.) After calculating the line of best fit using technology, students should be able to describe how strong the goodness of fit of the regression is, using "r".  
MGSE9-12.S.ID.9 Distinguish between correlation and causation. 

4. Two-frequency tables
Recall: converting fractions into decimals, To convert fractions into decimals, Divide the Numerator (the number on top) by the denominator (the number on the bottom.) Example: 6/24. 6÷24=0.25 So the answer is 0.25.
Recall: converting decimals to percents, Converting from a decimal to a percentage is done by multiplying the decimal value by 100. For example, 0.10 is 0.10 x 100 = 10% is x 100 = 67.5%. Note that the short way to convert from a decimal to a percentage by adding the percentage sign and moving the decimal point 2 places to the right.

5. Two way frequencies tables
Conditional Frequencies. The relative frequencies in the body of a two-way frequency table.
Bivariate data. Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team.
Joint Frequencies. Entries in the body of a two-way frequency table.
Trend. A change (positive, negative or constant) in data values over time.
Two-Frequency Table. A useful tool for examining relationships between categorical variables. The entries in the cells of a two-way table can be frequency counts or relative frequencies

6. Two-way frequency tables
Two-way frequency tables are a visual representation of the possible relationships between two sets of categorical data. The categories are labeled at the top and the left side of the table, with the frequency (count) information appearing in the four (or more) interior cells of the table. The "totals" of each row appear at the right, and the "totals" of each column appear at the bottom. Note: the "sum of the row totals" equals the "sum of the column totals" (the 240 seen in the lower right corner). This value (240) is also the sum of all of the counts from the interior cells.

7. Two-way frequency tables
vocabulary used to identify cell locations in two-way frequency tables:
Entries in the body of the table (the blue cells where the initial counts appear) are called joint frequencies. The cells which contain the sum (the orange "Totals" cells) of the initial counts by row and by column are called marginal frequencies. Note that the lower right corner cell (the total of all the counts) is not labeled as a marginal frequency.

8. Two-Way Relative Frequency Table: (displays "percentages")
When a two-way table displays percentages or ratios (called relative frequencies), instead of just frequency counts, the table is referred to as a two-way relative frequency table. These two-way tables can show relative frequencies for the whole table, for rows, or for columns. Notice that the relative frequencies may be displayed as a ratio, a decimal (to nearest hundredth), or percent (to nearest percent).

9. Two-way frequency table: Conditional frequencies
When a relative frequency is determined based upon a row or column, it is called a "conditional" relative frequency. To obtain a conditional relative frequency, divide a joint frequency (count inside the table) by a marginal frequency total (outer edge) that represents the condition being investigated. You may also see this term stated as row conditional relative frequency or column conditional relative frequency.

10. Conditional Relative Frequency for Rows:

11. Conditional Relative Frequency for Columns