Statistics
Solves Variance of a Dataset

Variance of a dataset

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Solves variance of any dataset

\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.

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

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.