Definition of variance?

Variance is a statistical measure that quantifies the amount of dispersion or spread in a set of data points. It is calculated as the average of the squared differences between each data point and the mean of the data set. A higher variance indicates that the data points are more spread out, while a lower variance indicates that the data points are closer to the mean.

Variance

In statistics, variance is a measure of how spread out a distribution of values is. It is defined as the average of the squared differences between each data point and the mean of the distribution.

Formula:

```
Variance = Σ(x - μ)^2 / (N-1)
```

Where:

- Σ: Summation operator
- x: Individual data point
- μ: Mean of the distribution
- N: Number of data points

Interpretation:

- A low variance indicates that the data points are tightly clustered around the mean.
- A high variance indicates that the data points are spread out widely from the mean.

Applications:

- Quantifying the dispersion of data in a probability distribution
- Comparing the variability of different distributions
- Hypothesis testing
- Estimating parameters in statistical models
- Risk analysis
- Financial forecasting