# Standard deviation

The next term is **standard deviation**. This value is similar to variance because **standard deviation** is the square root of variance. Therefore, the formulas will differ for the population and sample.

**Definition**

**Standard deviation** is a measure of how data is spread out in relation to the mean.

**68–95–99.7 rule**

If the **population follows a Normal Distribution**, we have the empirical 68-95-99.7 rule. According to this rule:

- Approximately 68% of the data falls within 1 standard deviation (σ) from the mean;
- About 95% of the data falls within 2σ of the mean;
- Nearly 99.7% of the data falls within 3σ of the mean.

When dealing with samples, the percentages might not be precisely accurate, but you can expect them to be quite close to the values in the rule, especially with larger sample sizes.

**Example**

To illustrate this, let's examine a sample of kitten weights measured in grams:

Take a look at the illustration. In this scenario, we are working with the following data:

- Mean value = 100 grams;
- Standard deviation (represented by the sigma symbol in the picture) = 20 grams.

As mentioned earlier, one standard deviation above and below the mean encompasses 68% of the values. In this instance, those values range from **mean - standard deviation = 100 - 20 = 80** to **mean + standard deviation = 100 + 20 = 120**.

Everything was clear?

Course Content

Learning Statistics with Python

## Learning Statistics with Python

2. Mean, Median and Mode with Python

4. Covariance vs Correlation

# Standard deviation

The next term is **standard deviation**. This value is similar to variance because **standard deviation** is the square root of variance. Therefore, the formulas will differ for the population and sample.

**Definition**

**Standard deviation** is a measure of how data is spread out in relation to the mean.

**68–95–99.7 rule**

If the **population follows a Normal Distribution**, we have the empirical 68-95-99.7 rule. According to this rule:

- Approximately 68% of the data falls within 1 standard deviation (σ) from the mean;
- About 95% of the data falls within 2σ of the mean;
- Nearly 99.7% of the data falls within 3σ of the mean.

When dealing with samples, the percentages might not be precisely accurate, but you can expect them to be quite close to the values in the rule, especially with larger sample sizes.

**Example**

To illustrate this, let's examine a sample of kitten weights measured in grams:

Take a look at the illustration. In this scenario, we are working with the following data:

- Mean value = 100 grams;
- Standard deviation (represented by the sigma symbol in the picture) = 20 grams.

As mentioned earlier, one standard deviation above and below the mean encompasses 68% of the values. In this instance, those values range from **mean - standard deviation = 100 - 20 = 80** to **mean + standard deviation = 100 + 20 = 120**.

Everything was clear?