Mean, Median, Mode

Formula / Rule

Mean, Median, Mode

Topic

Statistics

Formula

Mean (Arithmetic Average): $\frac{\text{Sum of values}}{\text{Number of values}}$

Median: To find the median, first arrange the data in ascending order.

If $n$ is odd: The median is the middle value.
If $n$ is even: The median is the average of the two middle values.

Mode: The most frequently occurring value.

Empirical Relationship: $\text{Mode} = 3(\text{Median}) - 2(\text{Mean})$ (for moderately skewed data)

Range = $\text{Max} - \text{Min}$

Variance = $\frac{\sum(x - \text{mean})^2}{n}$

Standard Deviation = $\sqrt{\text{Variance}}$

When to Use

Descriptive statistics, data analysis, and central tendency problems.

Worked Example

Data: $4, 7, 7, 9, 11, 13$

$\text{Mean} = \frac{(4+7+7+9+11+13)}{6} = \frac{51}{6} = 8.5$ $\text{Median} = \frac{(7+9)}{2} = 8$ (average of 3rd and 4th values after ordering) $\text{Mode} = 7$ (appears twice)