Variance in statistics is a measure of how much a set of values differs from the mean (average) of the dataset. It quantifies the spread or dispersion of data points in a dataset. Mathematically, the variance is the average of the squared differences between each data point and the mean. A higher variance indicates that the data points are more spread out, while a lower variance suggests they are closer to the mean.

The formula for variance differs depending on whether you are calculating for a population or a sample:

1. **Population Variance** (denoted as \( \sigma^2 \)):
   \[
   \sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2
   \]
   Where:
   - \( N \) is the total number of data points in the population.
   - \( x_i \) is each data point.
   - \( \mu \) is the population mean.

2. **Sample Variance** (denoted as \( s^2 \)):
   \[
   s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2
   \]
   Where:
   - \( n \) is the number of data points in the sample.
   - \( x_i \) is each data point in the sample.
   - \( \bar{x} \) is the sample mean.

The key difference between the two is the denominator: \( N \) is used for population variance, while \( n-1 \) is used for sample variance to account for the bias in using a sample to estimate a population parameter (this is called **Bessel's correction**).

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### Related Questions:
1. What is the difference between variance and standard deviation?
2. How do you calculate the mean and variance of a dataset?
3. What is Bessel's correction, and why is it applied to sample variance?
4. Can variance be negative? Why or why not?
5. How is variance used in real-world applications like finance or science?

**Tip:** Variance is always non-negative, as it involves squaring the differences, which ensures all values are positive or zero.

Explore the concept of variance in statistics, a crucial measure of data dispersion. Learn how to calculate population and sample variance, the key formulas, and the importance of Bessel's correction. Suitable for high school students in Grades 10-12.

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