Section 3.1
Measures of Central Tendency
Find the center of your data. Master the Mean, Median, and Mode, and understand why "average" isn't always what it seems.
1
The Arithmetic Mean
The "Average"
The sum of all values divided by the number of observations. It is the balancing point of the data.
Population Mean
Sample Mean
2
The Median (M)
The Middle Value
The value that splits the data in half. Crucial Step: You MUST order the data from smallest to largest first!
Case 1: Odd Number (n)
The median is exactly in the middle.
[1, 3, 5, 7, 9]
Case 2: Even Number (n)
The average of the two middle values.
[1, 3, 5, 7, 9, 11]
Mean of 5 & 7 = 6
3
The Mode
Most Frequent
The value that occurs with the greatest frequency. It is the only measure that works for Qualitative (Categorical) Data.
Unimodal: One peak (e.g., [1, 2, 2, 3])
Bimodal: Two peaks (e.g., [1, 2, 2, 3, 3, 4])
No Mode: No repeats (e.g., [1, 2, 3, 4])
4
Resistance & Skewness
Measure of Resistance
A measure is Resistant if extreme values (outliers) do not largely affect it.
Mean
NOT Resistant
Pulled towards the tail
Median
Resistant
Stays in the middle
Skewness Predictor
Skewed Left (Tail Left)
Symmetric (Bell)
Skewed Right (Tail Right)
Try It Yourself
Explore Central Tendency
Enter your own numbers below or try an example set to see how the Mean, Median, and Mode behave.
Adaptive Engine