Measuring spread with standard deviation

Mathematics · Data & Statistics · ages 16-17

Name ______________________ Date ____________

Find the mean of 2, 4, 4, 4, 5, 5, 7, 9.
Answer: ______________
Find the population variance of 2, 4, 4, 4, 5, 5, 7, 9.
Answer: ______________
The population variance of a data set is 4. What is its population standard deviation?
- 4
- 16
- 2
Find the mean of 2, 4, 4, 4, 5, 5, 7, 9.
Answer: ______________
The population variance of a data set is 4. What is its population standard deviation?
- 2
- 4
- 16
- 5
A data set has population variance 9. What is its population standard deviation?
Answer: ______________
Sets A = {4, 5, 6} and B = {1, 5, 9} share the mean 5. Which has the larger standard deviation?
- Set B
- Set A
- They are equal
- Cannot tell from this
Find the population variance of 2, 4, 4, 4, 5, 5, 7, 9.
Answer: ______________
Set P with 1, 9 and set Q with 4, 6. Ana says P has the larger standard deviation. Is Ana right?
Circle one: True False
Set P = {1, 9} and set Q = {4, 6}. Ana says P has the larger standard deviation. Is Ana right?
Circle one: True False

Answer key

For grown-ups. Fold this page away before handing over the rest.

5 · The values add to 40 and there are 8 of them, so the mean is 5.
4 · Squared gaps from the mean 5 add to 32, and 32 over 8 is 4.
2 · Standard deviation is the root of the variance, and root 4 is 2.
5 · The values add to 40 and there are 8 of them, so the mean is 5.
2 · Standard deviation is the root of the variance: root 4 = 2.
3 · Standard deviation is the root of variance, and root 9 is 3.
Set B · B spreads 4 each way while A spreads only 1, so B varies more.
4 · Squared gaps from the mean 5 add to 32, and 32 over 8 = 4.
True · Both average 5, but P strays 4 from the mean against 1 for Q.
True · Both average 5, but P strays 4 from the mean against 1 for Q, so P spreads more.