Describing Data with Mean, Median, and Mode
Finding the center
Measures of central tendency
Measures of center summarize a data set with one typical value. The main ones are mean, median, and mode.
Mean
The mean is the arithmetic average:
Median and mode
The median is the middle value when data are ordered. The mode is the most frequent value.
Choosing the best measure
Use the median when there are outliers, because extreme values can pull the mean away from the center.
Example data set
| Ordered data | Value |
|---|---|
| 1st | 2 |
| 2nd | 4 |
| 3rd | 4 |
| 4th | 10 |
What is the median of 2, 4, 4, 10?
The middle two values are 4 and 4, so the median is 4.
Correct answer: 4
What is the mean of 2, 4, 4, 10?
Add the values: , then divide by to get .
Correct answer: 5
Which measure is the most frequent value?
The mode is the value that appears most often.
Correct answer: Mode
Why might the median be better than the mean for house prices?
The median is resistant to extreme values.
Correct answer: Because house prices can have very large outliers that distort the mean.