What’s the difference between a standard deviation and a variance?

The **variance** and **standard deviation** are both measures of dispersion or spread in a dataset, but they differ in their interpretation and mathematical computation:

1. **Variance**: It measures how much the data points differ from the mean, on average, but in **squared units**. The formula for variance (\( \sigma^2 \) for a population or \( s^2 \) for a sample) is:
   \[
   \text{Variance} = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2
   \]
   where \( x_i \) represents each data point, \( \mu \) is the mean of the data, and \( n \) is the number of data points.

2. **Standard Deviation**: It is the square root of the variance and expresses the spread in the same units as the data itself. The formula for standard deviation (\( \sigma \) for a population or \( s \) for

Understand the difference between standard deviation and variance in statistics. Learn how variance measures the spread of data points in squared units, while standard deviation represents it in the same units as the data. Includes formulas and step-by-step explanations, suitable for Grades 9-12.

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