Mean
The mean is the sum of all values divided by how many there are. It is the usual meaning of average.
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Analogy
If everyone put their coins in a pot and shared them out equally, the mean is what each person gets.
Example
Values: 4, 8, 6, 5, 12Sum = 35Count = 5Mean = 35 / 5 = 7
In practice
Mean exam score, mean daily temperature and mean waiting time all use this formula.
Practice
Flashcards
- What is the formula for the mean?Add all values, then divide by the number of values.
- Which average resists extreme values: mean or median?The median. The mean is dragged toward extreme values.
Interview questions
- Data on household income has mean 52,000 and median 41,000. What does this tell you and which would you report?
- Mean above median suggests right skew
- A few high incomes pull the mean up
- Median is a better typical value
- Reporting both shows the gap
Questions people ask
How do you calculate the mean of a data set?
Add up every value, then divide by the number of values. For 4, 8, 6, 5 and 12 the sum is 35 and there are 5 values, so the mean is 7. In symbols the sample mean is written x-bar, equal to the sum of x divided by n.
Why is the mean sensitive to extreme values?
Every value contributes its full size to the sum, so one huge value drags the total up. Five house prices of 150, 160, 170, 180 and 900 thousand have a mean of 312 thousand, which describes none of the houses. The median resists this effect better.