What are Measures of Central Tendency?
Measures of central tendency are single values that describe the "center" or "typical value" of a data set. The three main measures are mean, median, and mode.
Mean (Average):
- Sum of all values divided by the number of values
- Formula: \(\bar{x} = \frac{\text{Sum of all observations}}{\text{Number of observations}}\)
- Most commonly used measure
Median (Middle Value):
- The middle value when data is arranged in order
- For odd number of observations: middle value
- For even number of observations: average of two middle values
- Not affected by extreme values (outliers)
Mode (Most Frequent):
- The value that occurs most frequently
- A data set can have one mode (unimodal), two modes (bimodal), or no mode
- Useful for categorical data
Comparison of Measures:
| Measure | Best Used When | Affected by Outliers? |
|---|---|---|
| Median | Data has outliers or is skewed | No |
| Mode | Data is categorical or has repeated values | No |