Lesson 16 of 1524
Describing data
An outlier pulls the mean and barely moves the median.
Practice this chapterThe mean is the sum divided by how many numbers you have. The median is the middle value once the list is ordered. The mode is the most frequent value. The range is the largest minus the smallest.
This chapter is the book’s short look at data, before a full statistics course. The shape of the list tells you which summary to trust.
Mean
mean = (sum of the values) / n
Add, then divide by the count.
Worked example
Find the mean and the median of 1, 2, 3, 4, 20.
- 1The mean uses every value. The sum is 1 + 2 + 3 + 4 + 20 = 30, and there are 5 numbers.
- 2Mean = 30 / 5 = 6.
- 3The median needs the list in order. This list already is. With 5 values, the middle position is the 3rd value, which is 3.
- 4The 20 raises the sum from 10 to 30, so it raises the mean. It does not change which position is in the middle, so the median stays 3.
Result: Mean 6, median 3
Why. The mean is the sum divided by the count, so the outlier 20 pulls it up to 6. The median is only the middle position of the ordered list, so that same outlier leaves it at 3.
If the list has an even count, the median is the average of the two middle numbers, not one of the endpoints.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.