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.