📊Mean, Median & Mode

Schools report average height, the news reports average salaries, and a shoe shop owner only asks which size sells out first. "Typical value" comes in three flavors, and each has its moment to shine.

One dataset, three spokespeople

Five students counted their pull-ups in one minute: $3, 4, 4, 5, 9$.

• Mean: add everything up, then share it evenly — $\dfrac{3+4+4+5+9}{5} = \dfrac{25}{5} = 5$
• Median: line the values up in order and take the one in the middle — $3, 4, \mathbf{4}, 5, 9$, so 4
• Mode: the value that shows up most often — 4 appears twice, so 4

Same dataset, yet the mean says 5 while the median and mode say 4. Who is to blame? That 9.

Outliers: the mean's weak spot

The 9 towers over the other scores. All by itself it drags the mean from 4 up to 5, while the median and mode don't move an inch. A value that stands apart like this is an outlier.

Salaries are the classic case. Five people earn 3,000; 4,000; 5,000; 6,000; and 50,000 yuan a month:

• Mean: $\dfrac{68000}{5} = 13600$ yuan — inflated by the last person;
• Median: 5,000 yuan — much closer to a "typical" income.

That is why income reports lean on the median. Shoe shops work the other way: the owner doesn't care about averages at all, only the mode — whichever size sells most gets restocked.

Median with an even count

When the dataset holds an even number of values, two of them share the middle, so the median is their average. Take $2, 4, 6, 10$: the middle pair is 4 and 6, and the median is $\dfrac{4 + 6}{2} = 5$.

Data Lab

+🗑 Clear4865389

Count

7

Mean

6.14

Median

6

Mode

8

Edit any value and all three measures weigh in again at once. Try dragging one value sky-high: which measures sprint after it, and which stand their ground?

Check yourself

✅

Quick quiz

↺ Try again

1. 1. What is the median of 2, 7, 9?

   769

2. 2. To describe a typical income in that one-tycoon group, which measure works best?

   MedianMeanMode

3. 3. What is the mode of 5, 5, 6, 7, 8?

   56.28