Mean, Median, Mode, Range

Why This Matters for Nursing: Understanding these statistics helps you interpret patient data. "The average blood pressure of patients on this medication..." or "What's the typical recovery time?" — these concepts show up in research, quality reports, and daily care decisions.

What You Need to Know

🧠 Memory Trick

Mean = "Mean people are AVERAGE" — add and divide

Median = "Median is in the MIDDLE" (like a road median)

Mode = "Mode is MOST" — most frequent value

Range = "Range is the REACH" — how far from low to high

Mean (Average)

Formula:

Mean = Sum of all values ÷ Number of values

Example: Find the mean of 4, 8, 6, 10, 12

Sum = 4 + 8 + 6 + 10 + 12 = 40 Count = 5 values Mean = 40 ÷ 5 = 8

Median (Middle)

Steps:

1. Order the values from smallest to largest
2. Find the middle:
3. Odd count: The middle number
4. Even count: Average of the two middle numbers

Example (Odd): Find the median of 7, 3, 9, 1, 5

1. Order: 1, 3, 5, 7, 9
2. Middle value: 5

Example (Even): Find the median of 4, 8, 2, 10

1. Order: 2, 4, 8, 10
2. Two middle values: 4 and 8
3. Average: (4 + 8) ÷ 2 = 6

Mode (Most Frequent)

Example: Find the mode of 3, 5, 7, 5, 9, 5, 2

Count each: 3(1), 5(3), 7(1), 9(1), 2(1) Most frequent: 5 (appears 3 times)

Special cases: - No mode: If all values appear equally (1, 2, 3, 4) - Multiple modes: If tie for most frequent (bimodal, multimodal)

Range (Spread)

Formula:

Range = Highest value - Lowest value

Example: Find the range of 15, 8, 22, 11, 19

Highest = 22, Lowest = 8 Range = 22 - 8 = 14

✏️ Worked Examples

Example 1: Complete Analysis

Problem: Find the mean, median, mode, and range of: 85, 90, 75, 90, 80, 90, 70

--- Finding the MEAN (average) ---

Step 1 — Add all values. 85 + 90 + 75 + 90 + 80 + 90 + 70. - 85 + 90 = 175 - 175 + 75 = 250 - 250 + 90 = 340 - 340 + 80 = 420 - 420 + 90 = 510 - 510 + 70 = 580

Step 2 — Divide by the count. There are 7 numbers. 580 ÷ 7 = 82.86 (rounded).

Mean = 82.86

--- Finding the MEDIAN (middle value) ---

Step 1 — Put the numbers in order from smallest to largest. 70, 75, 80, 85, 90, 90, 90.

Step 2 — Find the middle. There are 7 numbers, so the middle is the 4th number (3 on each side). Count to the 4th: 70, 75, 80, 85.

Median = 85

--- Finding the MODE (most frequent) ---

Step 1 — Count how many times each value appears. - 70 appears 1 time - 75 appears 1 time - 80 appears 1 time - 85 appears 1 time - 90 appears 3 times ← most frequent

Mode = 90

--- Finding the RANGE (spread) ---

Step 1 — Subtract lowest from highest. 90 - 70 = 20.

Range = 20