Measures of Central Tendency

Mean, median, and mode — what they measure, when they differ, and how to report them for dental variables like DMFT.

Back

What is "central tendency"?

Central tendency describes a single "typical" value for a dataset. In clinical datasets, the "best" center depends on whether your distribution is symmetric, skewed, or has outliers.

Mean (average)

Uses all values. Sensitive to outliers.

x̄ = (1/n) Σ xᵢ

Median (middle)

Robust to skew/outliers.

middle of sorted data

Mode (most frequent)

Most common value. Works for categorical too.

argmax frequency(x)

Why mean and median can differ

When data are right-skewed (common for counts like DMFT), a few high values pull the mean upward, but the median stays closer to the "typical" patient.

Symmetric example

mean = median = mode

All three are close when the distribution is roughly symmetric.

Right-skewed (DMFT-like)

median mean

Mean is pulled toward the long right tail.

Real Dental Scenario

DMFT Score Analysis — Step-by-step walkthrough

Scenario: A dental clinic screened 12 patients and recorded their DMFT (Decayed, Missing, Filled Teeth) scores:

0 1 2 2 3 3 4 5 6 8 12 15

Data is already sorted for this demonstration.

1 Calculating the Mean

Sum = 0

2 Finding the Median

n = 12 (even), so median = average of 6th and 7th values:

0 1 2 2 3 3 4 5 6 8 12 15

3 Identifying the Mode

Count frequency of each value:

Clinical Summary

Mean
5.08
Median
3.5
Mode
2, 3

Recommendation: Since DMFT data is right-skewed, report median (IQR) for this clinic. The mean of 5.08 overstates the typical patient experience due to a few patients with high DMFT scores (12, 15).

Interactive: compute + visualize

Paste comma-separated numbers and compute summary + histogram + boxplot.

Summary

Results will appear here.
Results will appear here.

Histogram

Median line (teal), mean dot (red), mode diamond (blue).

Boxplot (quick view)

Shows Q1–Q3 box, median line, whiskers, plus mean/mode markers.

How to report (dental examples)