### How do you find Mean, Median, Mode, Range, Standard Deviation and Variance?

**Mean** = Average = \overline{x} = Sum of all Numbers / Number of Numbers in List.

**Median **= Center Number of Ordered List

**Mode **= The most frequent Number in List

**Range**=Largest – Smallest Number in List

** Variance of Population ** \sigma^2 = \frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2 , \quad \mu = Population Mean

**Standard Deviation of Population** \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2} , \enspace \mu = Population Mean

** Variance of Sample ** s^2= \frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2 , \quad \overline{x} = Sample Mean

**Standard Deviation of Sample ** s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2} , \quad \overline{x} = Sample Mean

### How do I calculate Mean, Median, Mode and Range?

Let’s do an **Example with 7 numbers** (see right image)

a) To find the **Mean **we add up the 7 integers to get 80 and divide by 7 to get a Mean of 80/7 = 11.4 . Note: **Mean **is also called **Average**.

b) To find the **Median **we simply identify the center number to get a Median = 6. In case of 2 center numbers we will average them.

c) To find the **Mode **we simply identify the most common number to get a Mode = 1. Note: We may have 2 or more modes.

d) To find the **Range **we simply subtract the Minimum from the Maximum to get a **Range **= 42 – 1 =41.

e) **Outliers **are numbers that are way off.