Measures of Central Tendency & Dispersion

Reading Time: 8 Mins | Level: Intermediate

1. What is Central Tendency?

Central Tendency describes the central or typical value around which quantitative data points cluster:

• Mean (Average): The arithmetic center $\bar{x} = \frac{\sum x}{n}$. Highly sensitive to extreme outliers.
• Median (50th Percentile): The middle value when sorted. Resistant to outliers (robust).
• Mode: The most frequently occurring value in the dataset.

2. What is Statistical Dispersion?

Dispersion measures how widely the data points are spread out from the center:

• Range: $Max - Min$
• Variance ($s^2$): The average squared deviation from the mean: $s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$.
• Standard Deviation ($s$): The square root of variance: $s = \sqrt{s^2}$ (in original data units!).
• Interquartile Range (IQR): $Q3 - Q1$ (spread of middle 50%).