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Standard Deviation

Standard Deviation

Variance is a tricky statistic to use because its units are different from both the mean and the data itself. For example, the mean of our NBA dataset is `77.98`

inches. Because of this, we can say someone who is `80`

inches tall is about two inches taller than the average NBA player.

However, because the formula for variance includes *squaring* the difference between the data and the mean, the variance is measured in *units squared*. This means that the variance for our NBA dataset is `13.32`

inches squared.

This result is hard to interpret in context with the mean or the data because their units are different. This is where the statistic *standard deviation* is useful.

Standard deviation is computed by taking the square root of the variance. `sigma`

is the symbol commonly used for standard deviation. Conveniently, `sigma`

squared is the symbol commonly used for variance:

`$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{\sum_{i=1}^{N}{(X_i -\mu)^2}}{N}}$`

In Python, you can take the square root of a number using `** 0.5`

:

```
num = 25
num_square_root = num ** 0.5
```

We’ve written some code that calculates the variance of the NBA dataset and the OkCupid dataset.

The variances are stored in variables named `nba_variance`

and `okcupid_variance`

.

Calculate the standard deviation by taking the square root of `nba_variance`

and store it in the variable `nba_standard_deviation`

(on line 8). Do the same for the variable `okcupid_standard_deviation`

(on line 9).