1. The problem asks: Why do we need standard deviation if we already have variance? 2. Variance measures the average squared deviation from the mean, given by the formula: $$\text{Variance} = \sigma^2 = \frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2$$ where $x_i$ are data points and $\mu$ is the mean. 3. However, variance is in squared units of the original data, which can be hard to interpret. For example, if data is in meters, variance is in meters squared. 4. Standard deviation is the square root of variance: $$\text{Standard Deviation} = \sigma = \sqrt{\sigma^2}$$ 5. Taking the square root brings the measure back to the original units, making it easier to understand and compare variability. 6. In summary, standard deviation is preferred because it provides a measure of spread in the same units as the data, making interpretation more intuitive.