Keeper Ines solves the mystery of the 23. "That is M17, one of our volunteers. They help at the front desk almost every day."
Comet grabs the eraser. "Then let's delete that answer. It is messing up our average."
Wren puts a hand on the sheet. "What do you notice? It is a real, valid answer. M17 did visit 23 times."
"But it does not look like the other evening members," Comet says.
Nova projects two rows of numbers, one with the 23 and one without. "Would you like a hint?" she asks.
"Do not erase anything. Work out all three typical values both ways, and compare what moves."
The crew keeps M17's answer on the data sheet. On scratch paper, they work out the typical values without it, just to compare.
Without the 23, eight values are left: 1, 2, 2, 2, 3, 3, 4 and 5.
With eight values, no single value sits in the middle. The 4th value is 2 and the 5th is 3.
The crew uses the point halfway between them, 2.5. Then four values are below it and four are above it.
| Typical value | With M17 (9 values) | Without M17 (8 values) |
|---|---|---|
| Sum | 45 | 22 |
| Mean | 5 | 2.75 |
| Median | 3 | 2.5 |
| Mode | 2 | 2 |
Made-up data from the Commons Count story.
When data are lopsided, or skewed, the mean and the median are not the same.
The mean is pulled in the direction of the long tail. A few very extreme values cause this.
For skewed data, it is not obvious whether the mean, the median or the mode is most meaningful. All three are useful.
| Statement | True or false? |
|---|---|
| One extreme value can pull the mean far from most of the data. | ? |
| In skewed data, the mean and median are always the same. | ? |
| The crew should erase M17's answer because it is unusual. | ? |
| For skewed data, the mean, median and mode can all be useful. | ? |
Wise work, data analyst. Tomorrow in Count Lab you will choose which typical value to report.