Question

when comparing two datasets, if one has a standard deviation of 5 and the other 10, what does this imply?

a. the dataset with a standard deviation of 5 is normally distributed

b. the dataset with a standard deviation of 5 has more variability

c. they have the same mean

d. the dataset with a standard deviation of 10 has more variability

Explanation:

• Option a: Standard deviation value doesn't determine if a dataset is normally distributed. Normal distribution is about the shape of the distribution, not just standard deviation. So a is incorrect.
• Option b: A smaller standard deviation (5) means less variability, not more. So b is incorrect.
• Option c: Standard deviation and mean are different measures. Knowing standard deviations doesn't imply the means are the same. So c is incorrect.
• Option d: Standard deviation measures variability. A larger standard deviation (10) means the data points are more spread out, so the dataset with a standard deviation of 10 has more variability. This is correct.

Answer:

d. The dataset with a standard deviation of 10 has more variability