# What is variance in math

## Calculating standard deviation and variance simply explained

### Calculate variance

The variance is the root mean square deviation of the data series from its mean. To calculate the variance, you have to follow a simple scheme.

1. Calculation of the average

2. Calculation of the variance

To understand how the variance is calculated, consider the following example:

Katrin stops the time she needs from the train station home for five days. It receives the following data series:

**1st step: calculate the average**

In the first step we calculate the average. We add the individual minutes and divide by the number of days.

$ \ Large {\ frac {17 + 12 + 15 + 12 + 14} {5} = 14} $

**Step 2 calculate variance**

In order to calculate the variance, we now have to subtract the mean value from all the individual data and take the result to the power of two. Once we have done this, we add up the whole values again and divide by the number of days.

$ \ Large {\ frac {(17- \ textcolor {red} {14}) ^ 2 + (12- \ textcolor {red} {14}) ^ 2 + (15- \ textcolor {red} {14}) ^ 2 + (12- \ textcolor {red} {14}) ^ 2 + (14- \ textcolor {red} {14}) ^ 2} {5} = \ frac {9 + 4 + 1 + 4} {5} = 3.6} $

So we always divide by the number that we also divided by to calculate the average.

### Calculate standard deviation

Once we have calculated the variance, it is very easy to calculate the standard deviation.

The standard deviation is the root of the variance and is abbreviated as $ \ sigma $ (sigma).

To calculate the standard deviation for our example, we simply take the square root of the variance:

$ \ Large {\ sigma = \ sqrt [] {3,6} \ approx 1,9} $

**What does the standard deviation tell us?**

The standard deviation indicates the spread of the individual data around the mean. With their help we can say whether an average value is representative. In our example, the standard deviation from the mean (14 minutes) is approximately 2 minutes. So it always takes Katrin the same length of time to get home from the train station.

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