Both the mean and the median—often referred to as “averages”—are measurements of central tendency, but they provide essentially different answers.
The Arithmetic Mean
A dataset’s arithmetic mean is computed by adding together all of the numbers and dividing the result by the total number. The mean takes into account the entire magnitude of all data points since each number contributes to the total.
This characteristic, however, also renders the mean susceptible to being pulled in the direction of an extreme low or a single enormous number.
Mean (x̄) = Σx ÷ n
The Average
Sorting the dataset in ascending order and choosing the value that is exactly in the middle yields the median. The median is the midway of the two center numbers when the number of values is even.
Importantly, the median only considers relative ordering and order, not how severe the highest or lowest numbers are.
A specific salary comparison
The proprietor of a small boutique business makes $500,000, but the other five employees make $40,000, $45,000, $50,000, and $52,000.
- The arithmetic mean is $137,400 ($40k + $45k + $50k + $52k + $500k) ÷ 5.
- Median: $50,000 is the pay in the middle.
When a recruiter states that the “average salary is $137,400,” it is incredibly deceptive because four out of five employees make less than $55,000! The median salary of $50,000 is far more indicative of the average worker.
As a general rule, which should you choose?
- If the data (property prices, household income, website visit durations) is skewed or contains outliers, select the median.
- When the data (box office receipts, calorie intake tracking, standardized exam scores in a homogenous cohort) is essentially symmetric, lacks extreme anomalies, and each number truly contributes to a total sum, choose Mean.
Try it yourself
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