Sometimes a general description of a distribution does not give enough information, and a more precise way to talk about center or spread would be more useful. The mean, or average, is a number we can use to summarize a distribution.
We can think about the mean in terms of “fair share” or “leveling out.” That is, a mean can be thought of as a number that each member of a group would have if all the data values were combined and distributed equally among the members.
The table and diagram show how many liters of water are in each of five bottles.
To find the mean, first we add up all of the values, which we can think of as putting all of the water together: $1+4+2+3+0=10$.
To find the “fair share,” we divide the 10 liters equally into the 5 containers: $10\div 5 = 2$.
Suppose the quiz scores of a student are 70, 90, 86, and 94. We can find the mean (or average) score by finding the sum of the scores $(70+90+86+94=340)$ and dividing the sum by four $(340 \div 4 = 85)$. We can then say that the student scored, on average, 85 points on the quizzes.
In general, to find the mean of a data set with $n$ values, we add all of the values and divide the sum by $n$.