Measures of Central Tendency

mean

average

median

middle number

mode

number that appears most frequent

range

difference between the highest and lowest values in a data set

how to calculate mean

add up all the numbers in the data set and then divide by the total amount of numbers in the data set

how to calculate median

order the numbers in the data set from least to greatest, cross out each number on both ends until you find the middle number. If there’s 2 middle numbers add them together and then divide by 2.

how to calculate range

subtract the smallest number from the data set of the greatest number of the data set

pros: mean

Uses all data points

cons: mean

Sensitive to outliers

pros: median

• Resistant to outliers

• Appropriate for skewed data

cons: median

• Doesn’t use the magnitude of all values

• Less stable than the mean for symmetrical data

pros: mode

• The only measure for categorical data 

• Unaffected by outliers

cons: mode

• Can be far from the center

• May not exist

mean is best used for

• Symmetrical Distributions

• All numerical data where outliers are not a concern (eg: heights)

median is best used for

skewed distributions (eg: income, house prices)

mode is best used for

• Categorical data (eg: favourite colour, most popular product)

• numerical data to find the most common value

left skew (negative skew) example

age of death

normal distribution (symmetrical) example

height

right skew (positive skew) example

household income

symmetrical data =

no outlier

positive skew =

high outlier

negative skew =

low outlier