The formula to calculate the combined variance is:
\[ V_c = \frac{(n_1 - 1) \cdot V_1 + (n_2 - 1) \cdot V_2}{n_1 + n_2 - 2} \]
Where:
Combined variance is a statistical measure that represents the variance of two or more combined samples. It is used to understand the overall variability within a dataset that consists of multiple groups or samples. By calculating the combined variance, one can get a sense of how much the data points in the combined dataset deviate from the mean, taking into account the variances and sizes of the individual samples. This measure is particularly useful in fields such as quality control, research, and data analysis where understanding the combined variability of different groups is essential.
Let's assume the following values:
Using the formula:
\[ V_c = \frac{(30 - 1) \cdot 5.2 + (25 - 1) \cdot 4.8}{30 + 25 - 2} \approx 5.00 \]
The Combined Variance is approximately 5.00.
Let's assume the following values:
Using the formula:
\[ V_c = \frac{(40 - 1) \cdot 6.3 + (35 - 1) \cdot 5.9}{40 + 35 - 2} \approx 6.10 \]
The Combined Variance is approximately 6.10.
