Question

4 which of the following statements about a standard deviation is true? choose two correct answers. a standard deviation tells us how much the data deviates from the mean of the data. b none of the answer choices are correct. c the smaller the spread of data, the greater the standard deviation number. d standard deviation tells us what the standard number is in a data set. e a greater spread of data, the greater the standard deviation number.

Explanation:

• Option A: Standard deviation measures the dispersion of data from the mean, so this is correct.
• Option B: Since A and E are correct, B is wrong.
• Option C: Smaller data spread means smaller standard deviation, so C is wrong.
• Option D: Standard deviation is about dispersion, not a "standard number" in the dataset, so D is wrong.
• Option E: Greater data spread (more variability) leads to a larger standard deviation, so this is correct.

Answer:

A. Standard deviation tells us how much the data deviates from the mean of the data.
E. A greater spread of data, the greater the standard deviation number.