Statistics / Unit 2: Describing Distributions
2.1 Mean, Median and Mode
Notes
Measures of center describe a typical value.
- Mean $\displaystyle \bar{x} = \frac{\sum x}{n}$: add all values and divide by how many there are.
- Median: the middle value of the ordered list. With an even number of values, average the two middle ones.
- Mode: the most frequent value. A data set can have no mode, one mode or several.
- Example: 4, 7, 7, 10, 12 has mean $\displaystyle \frac{40}{5} = 8$, median 7 and mode 7.
Practice
What is the mean of 6, 8, 9, 12, 15?
The sum is 50 and $\displaystyle \frac{50}{5} = 10$. The value 9 is the median.
What is the median of 3, 9, 4, 12, 8, 5?
Order: 3, 4, 5, 8, 9, 12. Average the middle two: $\displaystyle \frac{5 + 8}{2} = 6.5$.
Shoe sizes of seven students are 7, 8, 8, 9, 9, 9, 10. The mode is:
Size 9 appears three times, more than any other size.
Ready for more? Take the Unit 2 test.