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Monte

Where is the middle

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Mean is the average. Median is the middle once sorted. Mode is the most common. The big idea: one extreme number drags the mean; the median barely moves.

Why it matters

The mean is where a seesaw balances. The median is the person standing in the middle of the line.

Pick the wrong one and you tell the wrong story: average pay with the CEO included describes nobody.

  • PricesHome prices are quoted as medians because a few mansions drag the mean up.
  • OperationsPlan totals with the mean delivery time; describe the typical order with the median.
  • RevenueA few big spenders pull up average revenue per user. Check the median.

Tennis example

Ranking points in the top 100: a few players hold huge totals, so the mean sits far above the median. For a typical top-100 player, use the median.

Check yourself

  1. Mean of 15, 7, 22, 7, 29, 11, 5, 0?

  2. Median of the same?

  3. Mode of 40, 55, 45, 70, 55, 60, 40, 35?

The trap

The mistake people make most on this one.

Duplicates count. In 15, 7, 22, 7, 29, 11, 5, 0 the 7 appears twice, and both stay in the sorted list.

Formulas

4 formulas and a way to remember them.
Mean
x bar = Σx / n for a sample, μ = Σx / N for a population
Median
Sort, take the middle; average the two middles if n is even
Mode
Most frequent value; none if all differ, bimodal if two tie
Skew
Right skew: mode < median < mean. Left skew: mean < median < mode.
Remember it
Mean is average salary with the boss in the room. Median is what the typical person makes. The mean chases the tail.

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