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Can you explain variance, standard deviation to me?

Feb 22, 2024

Can you explain variance, standard deviation to me?

Solution by Steps

step 1

To understand variance, we first need to know what it measures. Variance quantifies the spread of a set of numbers. It is calculated by taking the average of the squared differences from the Mean

step 2

Let's denote the Mean of the data set as

\mu

and each data point as

x_i

. The variance

\sigma^2

is calculated using the formula:

\sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i - \mu)^2

where

N

is the number of data points

step 3

Standard deviation is the square root of variance and provides a measure of the spread of the data in the same units as the data itself. It is denoted as

\sigma

and calculated using the formula:

\sigma = \sqrt{\sigma^2}

Answer

The variance is

\sigma^2

and the standard deviation is

\sigma

Key Concept

Variance and Standard Deviation

Explanation

Variance measures the spread of data points around the mean, and standard deviation is the square root of variance, providing a measure of spread in the original units of the data.