The pocket money that broke the average
Five pupils say how much pocket money they get each week: 4, 5, 5, 6 and 200 pounds. The last answer is a joke, or a typing slip, or a very rich pupil.
Add them up and the "average" is 44 pounds. Nobody in the group gets anything like that.
Key words
| Word | What it means |
|---|---|
| Outlier | a value far away from the rest of the data |
| Anomaly | anything in the data that does not fit the usual shape |
| Skewed data | data that bunches at one end with a long tail at the other |
| Mean | the total divided by how many values there are |
| Median | the middle value when the data is in order |
| Tail | the thin, stretched end of a skewed shape |
The cells students fill in are left blank in this preview.
By the end of this lesson
Note
I can spot an outlier, say what it does to an analysis, and say what skewed data is and how to handle it.
Starter
Have a go
Starter
3 questionsYour answers are marked here and are not kept. A college account keeps every student’s marks.
Try it: one value drags the mean
money = [4, 5, 5, 6, 200]
print("mean", sum(money) / len(money))
ordered = sorted(money)
print("median", ordered[len(ordered) // 2])
money = [4, 5, 5, 6, 7]
print("mean", sum(money) / len(money))
# The median barely moved. The mean jumped. Why?
Worked example: what one outlier does
| Data | Mean | Median | Range |
|---|---|---|---|
| 4, 5, 5, 6, 7 | 5.4 | 5 | 3 |
| 4, 5, 5, 6, 200 | 44 | 5 | 196 |
The cells students fill in are left blank in this preview.
What to do with an outlier
Never delete it just because it is odd. First ask why it is there.
- A mistake, such as a typing slip? Correct it, or remove it and say so.
- A real but rare case? Keep it, and report the median beside the mean.
- Not part of the group you study? Remove it and write down why.
Skewed data
Data is skewed when it bunches at one end. Most pupils spend little on snacks and a few spend a lot. The long tail goes to the right. This is right skew.
In right-skewed data the mean is pulled above the median. For a typical value, use the median.
Check
Have a go
Check
4 questionsYour answers are marked here and are not kept. A college account keeps every student’s marks.