Mean, Median, and Mode Calculations

Three measures of center

Mean (average): Add all values, divide by the count.

Median: Sort the data, take the middle value (or average of two middle values if even count).

Mode: The most frequently occurring value.

Step-by-step: {3, 7, 7, 2, 9, 4, 7, 5}

Step 1 — Sort: {2, 3, 4, 5, 7, 7, 7, 9}

Step 2 — Mean:

$\bar{x} = \frac{2 + 3 + 4 + 5 + 7 + 7 + 7 + 9}{8} = \frac{44}{8} = 5.5$

Step 3 — Median: 8 values (even count), so median = average of 4th and 5th values:

$\text{median} = \frac{5 + 7}{2} = 6$

Step 4 — Mode: 7 appears 3 times (most frequent). Mode = 7.

Summary

• Mean = 5.5 (sensitive to extreme values)
• Median = 6 (robust to outliers)
• Mode = 7 (most common value)

When to use which

• Mean when data is symmetric with no outliers.
• Median when data is skewed or has outliers (e.g., income data).
• Mode for categorical data or finding the most popular option.

Try it in the visualization

The sorted data is displayed with markers for mean (red line), median (green line), and mode (blue highlight). Drag values to see how each measure responds.