Average (Mean)
A single number taken as representative of a list of numbers, calculated by dividing the sum of the values by the number of values.
Definition
An Average (specifically the arithmetic mean) is a single number taken as representative of a list of numbers. It is calculated by dividing the total sum of all the values in a set by the number of values in that set.
Why It Matters
Averages are used everywhere to summarize large datasets. Whether it's a student's GPA, the average temperature for a month, or the average cost of a home in a specific city, averages allow us to digest complex data quickly.
The Flaw of Averages
While useful, an average can be highly skewed by outliers (extreme highs or lows). For example, if nine people in a room earn $50,000 a year, and one person earns $10 million, the "average" salary in the room is over $1 million. In cases with extreme outliers, looking at the median (the literal middle number) often provides a more accurate picture of reality.
Practical Example
Calculating an Average Score
A student takes 4 tests and gets the following scores: 80, 90, 85, and 100.
- Step 1: Sum the numbers. 80 + 90 + 85 + 100 = 355
- Step 2: Count the values. There are 4 test scores.
- Step 3: Divide. 355 ÷ 4 = 88.75 Average Score.
Frequently Asked Questions
Is the average the same as the median?
No. The average is the mathematical sum divided by the count. The median is the literal middle number in a sorted list.