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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

step 2

To calculate the variance (

\sigma^2

) of a set of numbers, we first find the mean (

\mu

) of the set

step 3

Next, we subtract the mean from each number in the set, square the result, and then find the average of these squared differences. The formula for variance is:

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

where

x_i

represents each number in the set, and

n

is the total number of numbers in the set

step 4

Standard deviation (

\sigma

) is the square root of the variance. It is also a measure of spread and is more commonly used because it is in the same units as the original data. The formula for standard deviation is:

\sigma = \sqrt{\sigma^2}

Answer

Variance (

\sigma^2

) is the average of the squared differences from the Mean. Standard deviation (

\sigma

) is the square root of the variance.

Key Concept

Variance and standard deviation measure the spread of a data set.

Explanation

Variance gives the average squared deviation from the mean, while standard deviation provides a measure of spread in the same units as the data.