In this episode you will
- Calculate mean and median
- Choose the right average for skewed data
Ten people sit in a café, each earning $50,000 a year. A billionaire walks in and orders a coffee. The average income in the room just went up by about ninety million dollars, and not one of the original ten is any richer. This episode is about why that happens, and which number you should have used.
Part 1
Three kinds of average
- The mean adds every value and divides by how many there are.
- The median is the middle value when everything is sorted: half the values are below it, half above.
- The mode is the most common value.
For tidy, symmetric data they are close together. When data is lopsided, they come apart, and that gap is information.
Part 2
Skew pulls the mean
Data is skewed when a long tail stretches out on one side. Incomes, house prices, company revenues, website session lengths: most real-world quantities with a floor at zero and no ceiling are right-skewed.
The mean is sensitive to every value, so a few extreme ones drag it toward the tail. The median ignores how extreme the extremes are, which makes it robust. When someone reports a mean for skewed data, ask for the median too.
Part 3
When the mean is still right
The mean isn't wrong, it answers a different question. If you need totals, such as budget planning or revenue forecasts, the mean is the right tool: total = mean × count.
A useful rule: use the median to describe a typical case, and the mean to reason about totals.
Nine salaries and one outlier
A team of ten has nine people earning $50,000 and one earning $1,000,000.
- Mean: (9 × $50,000 + $1,000,000) ÷ 10 = $1,450,000 ÷ 10 = $145,000.
- Median: sort the values; the 5th and 6th are both $50,000, so the median is $50,000.
- Mode: $50,000, which appears nine times.
A job advert saying average salary $145,000 would be accurate and badly misleading: nine out of ten people earn about a third of that. But if finance needs the total payroll, the mean is exactly what they want: $145,000 × 10 = $1.45 million.
Written by Edusodes editors.Researched and written by our editorial team.
Key takeaways
- 1Mean, median and mode answer different questions about the same data.
- 2Extreme values pull the mean; the median is robust to them.
- 3For skewed data such as incomes or prices, report the median for a typical case.
- 4Use the mean when you need to reason about totals.
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