Q.If the variance of a data is 121, then the standard deviation of the data is _______.

The key idea here is the fundamental relationship between variance and standard deviation, two crucial measures of data dispersion.

Variance ($\sigma^2$) quantifies the average of the squared differences from the mean, indicating how spread out the data points are. However, its units are the square of the original data units, making it less intuitive for direct interpretation. …

When we analyze a set of data, we often want to understand not just its central tendency (like the mean), but also how spread out the data points are. This spread or dispersion is crucial for understanding the variability within the data. Two common measures for this are variance and standard deviation.

Variance ($\sigma^2$) quantifies the average squared difference of each data point from the mean. While it's a powerful mathematical tool, its units are the square of the original data units, which can make it difficult to interpret directly in the context of the original data. For example, if your data is in meters, the variance will be in square meters.

Standard deviation ($\sigma$) addresses this interpretability issue. It is simply the positive square root of the variance. By taking the square root, the standard deviation returns to the original units of the data, making it much easier to understand the typical deviation of data points from the mean. A larger standard deviation indicates greater spread in the data, while a smaller one indicates data points are clustered closer to the mean.

Let's apply this concept to the given problem.

1. Identify the given information: We are given that the variance of the data is 121. So, $\sigma^2 = 121$. …