Variance

High school (ages 12+)
Mathematics & Numbers

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Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/variance

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the population variance formula?σ² = Σ(xi - μ)² / N
2. What is the sample variance formula?s² = Σ(xi - x̄)² / (n-1)
3. What does variance tell us about numbers?Variance shows how far numbers spread from the average. If all numbers are the same, variance is zero. A bigger variance means numbers are more spread out.
4. How do we calculate variance for a whole group of numbers?First find the average (mean). Then subtract the mean from each number, square each difference, and average those squares. That average is the variance.

Population Mean (μ): The average of all values in an entire group or population.
Sample Mean (x̄): The average of values in a subset (sample) taken from a larger population.
Bessel's Correction: The use of n-1 in the denominator for sample variance to provide an unbiased estimate of population variance.
Heteroskedasticity: A condition where the variance of the errors or residuals is not constant across all levels of the independent variables.