Range, Variance, and Standard Deviation

How far from typical is typical?

12 problems · about 22 minutes · TEKS P.S.1.D, S-ID.A.2

What this lesson teaches

The student computes and interprets range, variance and standard deviation.

Range is quick but depends only on the extremes.
Variance averages the squared deviations; the standard deviation is its square root.
A standard deviation is roughly the typical distance from the mean.

Straightforward practice. Get the method working first.

5 problems

Variance is 36. What is the standard deviation?
Answer 6
Why 6.
Why are deviations squared?
Answer Otherwise the positives and negatives cancel to zero.
Why Raw deviations always sum to zero.
Data 5, 9, 14. Range?
Answer 9
Why 14 − 5.
Variance is 25. What is the standard deviation?
Answer 5
Why √25.
Standard deviation is 7. What is the variance?
Answer 49
Why 7².

The same ideas with more to keep track of.

3 problems

Data 4, 4, 4. Standard deviation?
Answer 0
Why No spread at all.
Mean 10, one value 13. What is that deviation?
Answer 3
Why 13 − 10.
What do all the deviations from the mean add up to?
Answer 0
Why That is why squaring is needed.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Put the standard deviation calculation in order.
Answer 1. Find the mean. 2. Subtract the mean from each value. 3. Square the deviations and average them. 4. Take the square root.
Why Nothing can be measured from the mean until it is known.
Variance 100. Standard deviation?
Answer 10
Why √100.
The Range: Data 3, 8, 15, 20. What is the range?
Answer 17
Why 17.
The Identical Set: Data 6, 6, 6, 6. What is the standard deviation?
Answer 0
Why 0.