Lesson 23 of 1524
Descriptive statistics
Picture the sample before you infer anything, and let the median resist outliers.
Practice this chapterA histogram shows shape. A box plot shows the five-number summary: minimum, first quartile, median, third quartile, and maximum. The interquartile range is Q3 − Q1.
The sample standard deviation divides the squared deviations by n − 1, not by n. A long right tail usually pulls the mean above the median.
Mean
x̄ = (sum of the values) / n
The sample mean uses every value. The median uses the middle position.
Worked example
For 2, 4, 4, 7, 8, name the median and the mean.
- 1Order the list before you look for the median. This list is already ordered: 2, 4, 4, 7, 8.
- 2There are 5 values, so the middle position is the 3rd. That value is 4. The repeated 4 does not change which position is the middle.
- 3The mean uses every value. The sum is 2 + 4 + 4 + 7 + 8 = 25.
- 4Divide by the count: 25 / 5 = 5. The mean is 5.
- 57 and 8 are above the middle, so they pull the mean up from 4 to 5. The median stays at the middle position.
Result: Median 4, mean 5
Why. The median is the middle value of the ordered list, which is 4. The mean is the sum divided by how many numbers there are, 25 / 5 = 5. The mean is higher because it has to account for 7 and 8, and the median does not.
Sorting is required before you pick the median. The middle of an unsorted list is not the median.
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.