Measures of Center

Explore the statistics of central tendency. Drag and place observations to observe in real-time how the Mean, Median, and Mode behave and diverge in skewed distributions.

Interactive Sandbox

Symmetrical & Skewed Distributions

Click on any column to place a dot. Click and drag an existing dot to adjust its value, or right-click a dot to delete it. Compare the three indicators of center.

CLICK to add | DRAG to move | RIGHT-CLICK to remove
Mean (Balance Fulcrum)
Median (Middle Value)
Mode (Tallest Column)
Left Half of Dataset
Right Half of Dataset

1. Distribution Presets

2. Load Custom Dataset

Enter comma-separated integers between 0 and 15:

Algebraic Solver

Central Tendency Resolution Steps

Trace how the sorted dataset is evaluated mathematically to determine each metric.

Trace Calculations

Please add observations to see solver trace.

Summary Statistics


Mean (Average)

Sum / N
0.00

Median (Middle)

50th Percentile
0.0

Mode (Peak)

Highest Frequency
None

Sample Count (N)

Observations
0
Evaluation

Measures of Center Quiz

Test your understanding of skewness directions, how outliers distort averages, and which metrics are robust.

Question 1 of 5 Score: 0/0

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Correct Answer!

Explanation text...

Distribution Shape Cheat Sheet


  • Symmetric: Mean, Median, and Mode are exactly or approximately equal. The distribution balances perfectly in the center.
  • Skewed Right (Positive): Outliers pull the Mean to the right of the Median. Order: Mode < Median < Mean.
  • Skewed Left (Negative): Outliers pull the Mean to the left of the Median. Order: Mean < Median < Mode.
  • Outlier Robustness: The Median is highly resistant to extreme outliers. The Mean is sensitive and easily pulled.