Bivariate Frequency Distribution
Class 11 Statistics — Two-Way Frequency Tables and Construction
What is a Bivariate Distribution?
If one variable has m classes and the other has n classes, the bivariate frequency table will have m × n cells.
| Aspect | Univariate | Bivariate |
|---|---|---|
| Meaning | Data classified on the basis of a single variable | Data classified on the basis of two variables |
| Purpose | Describes a particular variable | Determines empirical relationship between two variables |
| Alternate Name | One-way frequency distribution | Two-way frequency distribution |
| Example | Height of students in a class | Height and Weight of students in a class |
Think about it
Your teacher wants to know if students who score high in Accounts also score high in Economics. A univariate table would just list Accounts marks. A bivariate table cross-classifies each student’s Accounts marks with their Economics marks — revealing the relationship between the two subjects.
Construction of a Bivariate Table
Follow these 4 steps to construct a bivariate frequency distribution.
Identify all distinct values for Variable X (columns) and Variable Y (rows). The table will have m × n cells.
Variable X: Marks in Accounts
25, 26, 27, 28 → 4 distinct values
Variable Y: Marks in Economics
19, 20, 21, 22 → 4 distinct values
The table will have m × n = 4 × 4 = 16 cells.
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Loss of Information
A frequency distribution summarizes raw data to make it simpler and easier to understand. However, it does not show individual data values, so some information is lost. For example, if the class 10–20 contains values 12, 15, 16, 18, 14, 19, we record only the frequency 6, not the actual values. Statistical results are based on class marks rather than the exact data, leading to considerable loss of information from the original data.
Key Takeaways
- Raw data is organized into a frequency distribution to make it simpler and easier to understand.
- The process of classification and tabulation leads to some loss of information because individual data values are not preserved.
- In calculations, all values in a class are assumed equal to the class mark (middle value), so statistical results are approximations.
- Bivariate distributions extend this same logic to two variables simultaneously.
Key Takeaways
Key Takeaways
- A bivariate frequency distribution classifies data on two variables simultaneously, creating a two-way table.
- The table has m columns (values of Variable X) and n rows (values of Variable Y), with m × n cells.
- Four construction steps: Identify variables ? Set up grid ? Tally each observation ? Compute marginals.
- Row totals = Marginal Distribution of Y; Column totals = Marginal Distribution of X.
- The sum of row totals always equals the sum of column totals = total number of observations (N).
- Grouping data into frequency distributions always involves some loss of information compared to raw data.