Mean, Median, Mode Relationship in Frequency Distribution

For moderately skewed frequency distributions, there is a known empirical relationship that connects the mean, median, and mode. This formula is useful for estimating one of these central tendency measures if the other two are known.

The standard empirical formula is generally stated as:

$ \text{mode} = 3 \times \text{median} - 2 \times \text{mean} $

To match the format of the options provided, we can rearrange this formula algebraically to express the mean in terms of the median and mode.

Steps to Find Mean Formula

1. Start with the standard empirical formula: $ \text{mode} = 3 \times \text{median} - 2 \times \text{mean} $
2. Rearrange the terms to isolate the part containing the mean: $ 2 \times \text{mean} = 3 \times \text{median} - \text{mode} $
3. Solve for the mean by dividing both sides by 2: $ \text{mean} = \frac{3 \times \text{median} - \text{mode}}{2} $

This derived formula directly corresponds to option A.