9.3 Mean, Median, Mode & Range

The Four Measures

A list of numbers is hard to interpret on its own. Four statistics compress it into something a nurse or a test-taker can act on:

Mean: The Arithmetic Average

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

Worked Example: Systolic BP Readings

A patient's systolic BP over five readings: 118, 122, 130, 126, 114 mmHg.

Step 1: Sum: 118 + 122 + 130 + 126 + 114 = 610. Step 2: Count: 5 readings. Step 3: Divide: 610 ÷ 5 = 122 mmHg.

The mean systolic BP is 122 mmHg.

The Outlier Problem

Add a sixth reading of 190 mmHg (a possible cuff error or a hypertensive spike). New sum = 610 + 190 = 800. New count = 6. New mean = 800 ÷ 6 ≈ 133.3 mmHg.

One extreme reading pulled the mean up by more than 11 mmHg. This is why the mean is called sensitive to outliers. In nursing, a single outlier in a vital-signs series is often a measurement error, and reporting the mean uncritically would misrepresent the patient's typical state.

Median: The Middle Value

The median is the middle of an ordered list. It is robust — outliers do not move it much, because it depends on position, not on the size of every value.

Odd Count

Order the five original BP readings: 114, 118, 122, 126, 130. The middle value (third of five) is 122 mmHg. Here the mean and median agree.

Even Count — Average the Two Middle Values

Take six readings: 114, 118, 122, 126, 130, 190. With an even count, there is no single middle value. Take the two middle values — the third and fourth — and average them.

Step 1: The two middle values are 122 and 126. Step 2: Add and divide by 2: (122 + 126) ÷ 2 = 248 ÷ 2 = 124 mmHg.

Compare this to the mean with the outlier (133.3 mmHg). The median barely moved (122 → 124), while the mean jumped by 11. This is the classic reason to prefer the median for skewed data.

Quick Median Procedure

1. Sort the data from smallest to largest.
2. Count the values, n.
3. If n is odd, the median is the value at position (n + 1) ÷ 2.
4. If n is even, the median is the average of the values at positions n ÷ 2 and (n ÷ 2) + 1.

Mode: The Most Frequent Value

The mode is the value that appears most often. A data set can have:

• No mode — every value appears exactly once.
• One mode — one value appears more often than the others.
• Two or more modes — two or more values tie for the highest frequency.

Worked Example: Heart Rates

Readings: 72, 80, 72, 88, 76, 80, 80.

Count each value: 72 appears 2 times, 80 appears 3 times, 76 appears 1 time, 88 appears 1 time. The mode is 80 bpm because it appears most often.

Why Mode Matters for Categorical Data

You cannot compute a mean or median for categories like blood type or admission reason — you cannot order them or average them. The mode is the only average that works. "The most common blood type among our patients is O+" is a mode statement.

Range: The Spread

The range is the simplest measure of spread: maximum − minimum.

Worked Example

BP readings: 114, 118, 122, 126, 130. Max = 130, min = 114. Range = 130 − 114 = 16 mmHg.

With the outlier 190 added: max = 190, min = 114. Range = 190 − 114 = 76 mmHg.

The range is also sensitive to outliers — one extreme value stretches it dramatically. Like the mean, treat the range with caution when the data has a clear outlier.

When to Use Which Measure

A classic NEX scenario: a patient's temperatures are 98.6, 98.8, 99.0, 99.2, and 103.1. The mean (99.74 °F) suggests a fever, but four of five readings are below 99.5. The median (99.0 °F) better reflects the typical value, and the outlier (103.1) may be a spike or a measurement error worth rechecking rather than a true baseline.