Here's an example of what you could use as data: the length of garden earthworms.
Collect a random sample of 15 earthworms from the garden and measure each of their lengths in millimetres (you may need someone to keep the worms straight while you measure). Return them to the garden after measuring.
Add up all 15 measurements, then divide by 15 to get x̅, the average (mean) length.
Make a table with 15 rows of data. First column will be length.
Second column will be each of the lengths minus the mean. Some results will be negative.
Check that the sum of values in the second column is zero.
Third column is the square of the second column values (all squares are positive).
Sum the squares in the third column. Since this is a sample, divide the sum by 14 (1 less than the sample size) to get the variance (spread of data). Take the square root of this to get the sample standard deviation s.
In the fourth column compute (X-x̅)/s using X-x̅ from the second column. The results will contain positive and negative numbers.
In the fifth column place a checkmark (✔️) for those values which are greater than or equal to 2 or less than (more negative than) -2.
Count the number of checked values and divide by 15. Multiply this fraction by 100 to get the percentage.
Consult a reference book contain population statistics about the length of earthworms in your part of the world (or similar climate). Use Key Fact 3.2 as a guide on what to do next. You can judge statistically whether your results are a typical sample of earthworm lengths, or whether they are unusual.
