Measures of Center

Mean (Average)

The mean is the sum of all values divided by the number of values.

$\text{Mean} = \frac{\text{sum of all values}}{\text{number of values}}$

Example: Mean of $\{3, 7, 4, 10, 6\}$ $\text{Mean} = \frac{3 + 7 + 4 + 10 + 6}{5} = \frac{30}{5} = 6$

Median

The median is the middle value when data is ordered.

Steps:

1. Put data in order from least to greatest
2. If odd number of values: middle value
3. If even number of values: average of two middle values

Example: Median of $\{3, 4, 6, 7, 10\}$ is 6 (middle value)

Mode

The mode is the value that appears most often.

Example: Mode of $\{2, 3, 3, 5, 7, 3, 9\}$ is 3 (appears 3 times)

• No mode: all values appear equally
• Multiple modes: if multiple values tie for most frequent

Range

The range is the difference between the maximum and minimum values.

$\text{Range} = \text{max} - \text{min}$

Example: Range of $\{2, 5, 8, 12, 3\}$ is $12 - 2 = 10$