Variance

Variance is a measure of how much the values in a data set differ from the mean (average) value. It is a measure of the spread or dispersion of the data.

The formula to calculate the variance of a data set is:

$\sigma^2 = \frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n}$

Where:

• $\sigma^2$ = variance
• $x_i$ = individual data values
• $\mu$ = mean of the data set
• $n$ = number of data values

To calculate the variance, follow these steps:

1. Find the mean of the data set.
2. Subtract the mean from each data value, then square the result.
3. Find the sum of all the squared differences.
4. Divide the sum by the number of data values to get the variance.

Properties of Variance:

• Variance is always non-negative.
• If all the data values are identical, the variance is 0.
• If the data values are spread out, the variance is high.

It's important to understand variance because it helps in understanding the data distribution and making decisions based on the variability of the data.

Study Guide:

1. Understand the concept of mean and how it is calculated.
2. Learn the formula for variance and understand each component of the formula.
3. Practice calculating variance for different data sets.
4. Understand the properties and significance of variance in real-world scenarios.
5. Work on solving problems and applying variance in different contexts.

By understanding and practicing variance, you'll be able to analyze and interpret the spread of data in a meaningful way.