Why Averages Lie
A single extreme observation changes the mean. The median does not move. Watch the numbers, then try the experiment.
Why Averages Lie · Animated storyboard
This is a silent, interactive preview of the first video, not a recorded lecture. Start playback or move the timeline manually. All figures are fictional and expressed in thousands of US dollars.
What happens when one observation becomes extreme?
Paused. Narration has not been recorded.
Five amounts: 40, 45, 50, 55, 60 thousand dollars. Mean 50.0; median 50.0.
Read the complete storyboard transcript (all timed text and descriptions)
- 0–12 seconds · Why Averages Lie
What happens when one observation becomes extreme?
Begin with five fictional annual incomes, in thousands of dollars.
- 12–28 seconds · Five observations
40, 45, 50, 55, and 60 thousand dollars.
The five amounts are synthetic, not actual household records.
- 28–43 seconds · Mean and median agree
The mean is 50. The median is also 50.
Both center measures agree when the fifth observation is 60.
- 43–61 seconds · One observation changes
Move the fifth observation from 60 to 600.
Only the last observation changes. The other four remain fixed.
- 61–79 seconds · Different answers, same data
The mean jumps to 158. The median remains 50.
The mean follows the extreme value; the median remains the middle observation.
- 79–95 seconds · Neither number is a lie
A mean is a balancing point. A median is the middle ordered value.
Both calculations are correct, but they summarize different aspects of the data.
- 95–106 seconds · Now try it yourself
Predict what will happen before moving the outlier slider.
Visit the center-and-spread lab, vary the fifth observation, and explain the result.
Starting values: 40, 45, 50, 55, 60; mean 50, median 50. Final values: 40, 45, 50, 55, 600; mean 158, median 50. The sequence illustrates different summaries of the same fictional observations.
What to learn from the animation
The two sets of numbers are fictional annual incomes expressed in thousands of dollars. The mean goes from 50 to 158 when the fifth value changes from 60 to 600; the median stays at 50. Both measures are mathematically correct, but the mean is much more sensitive to extremes.
Read the full lesson and manipulate the data →