Statistics: Mean, Median, Mode & Range

Week 9 · Statistics

Learn to find and use the four key measures that describe a data set.

The Four Measures\n\n### Mean (Average)\nAdd all values, then divide by how many there are.\n\nData: {4, 7, 3, 8, 8} → Sum = 30, Count = 5 → Mean = 30 / 5 = 6\n\n### Median (Middle Value)\nSort the data, then find the middle value.\n- Odd count: middle number is the median.\n- Even count: average of the two middle numbers.\n\nData: {3, 4, 7, 8, 8} → Middle = 7\n\n### Mode (Most Frequent)\nThe value that appears most often. A data set can have more than one mode, or no mode.\n\nData: {3, 4, 7, 8, 8} → 8 (appears twice)\n\n### Range (Spread)\nRange = Maximum - Minimum\n\nData: {3, 4, 7, 8, 8} → Range = 8 - 3 = 5\n\n## Which Measure to Use?\n- Use mean when data has no extreme outliers.\n- Use median when there are very high or very low values.\n- Use mode for categories or most popular items.

Example 1

📝 Find the mean of {6, 10, 8, 12, 14}.

✓ Answer: 10

Sum = 6 + 10 + 8 + 12 + 14 = 50. Count = 5. Mean = 50 / 5 = 10.

Example 2

📝 Find the median of {7, 2, 9, 4, 1, 6, 3}.

✓ Answer: 4

First sort: {1, 2, 3, 4, 6, 7, 9}. With 7 values, the median is the 4th value: 4.

⚠️Forgetting to sort the data before finding the median
⚠️Averaging only the two middle numbers when there is an odd count — with an odd count there is one exact middle
⚠️Confusing mode with median — mode is most frequent, median is the middle value