Subject - Statistics.

Variance, Standard Deviation

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Reading time 3 mins

** Student Question**

Can you explain variance and standard deviation to me?

Solution

  • 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 = (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 = √{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.

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