Variance Solver

Statistics
Solves Variance of a Dataset

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Solves variance of any dataset

variance formula

\sigma^2=\frac{\sum_{ }^{ }\left(x-\overline{x}\right)^2}{n-1}

Variance measures how spread out the numbers in a data set are from the average. It tells us how much the numbers differ from the mean.

Example

Let’s say we have a list of numbers: 2, 4, 6, 8, 10

Step 1: Calculate the mean (average) of the numbers: (2 + 4 + 6 + 8 + 10) / 5 = 6

Step 2: Calculate the difference between each number and the mean:
2 – 6 = -4
4 – 6 = -2
6 – 6 = 0
8 – 6 = 2
10 – 6 = 4

 

Step 3: Square each difference:

(-4)^2=16, \\ (-2)^2=4, \\ (-0)^2=0, \\ (2)^2=4, \\ (4)^2=16

 

Step 4: Calculate the average of the squared differences:

\frac{16+4+0+4+16}{5} = 8

 

Simpler Explanation

  • Imagine you have a group of friends who all have different ages. The variance tells us how spread out their ages are from the average age.
  • If they are all close to the same age, the variance is small.
  • If they are all different ages, the variance is larger.

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