Explain variance and standard deviation.

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Variance and standard deviation are two key statistical measures that describe how spread out or dispersed the data is in a dataset.

✅ 1. Variance (σ² or s²)

  • Definition: Variance measures the average squared difference between each data point and the mean.

  • Formula (for a population):

    σ2=1N∑i=1N(xi−μ)2\sigma^2 = \frac{1}{N} \sum_{i=1}^{N}(x_i - \mu)^2

    (For a sample, divide by n - 1 instead of n.)

  • Interpretation: A higher variance means data points are more spread out from the mean. A lower variance means they are closer together.

🧠 Example:
If test scores vary from 60 to 100, variance will be high. If they cluster around 85, variance is low.

✅ 2. Standard Deviation (σ or s)

  • Definition: Standard deviation is the square root of variance. It gives the average distance each data point is from the mean.

  • Formula:

    σ=σ2\sigma = \sqrt{\sigma^2}

  • Interpretation: It’s easier to understand than variance because it’s in the same units as the original data.

🧠 Example:
If standard deviation of salaries is $2,000, most people earn within $2,000 of the average salary.

✅ Summary:

  • Variance tells how spread out data is.

  • Standard deviation shows that spread in more interpretable terms.
    Both are essential for understanding data consistency and variability.

Read More

What is the difference between population and sample?

Explain the concept of Naive Bayes classifier. How does it work?

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