The question asks about which statement regarding standard deviation is true. Let's analyze each option:

1. Option A: "A greater spread of data, the greater the standard deviation number."

   • True. Standard deviation measures the spread or dispersion of data. If the data points are more spread out from the mean, the standard deviation will be larger.

2. Option B: "The smaller the spread of data, the greater the standard deviation number."

   • False. This is the opposite of how standard deviation works. A smaller spread would result in a smaller standard deviation.

3. Option C: "Standard deviation tells us what the standard number is in a data set."

   • False. This statement is vague and incorrect. Standard deviation measures the variability, not a "standard number" in the data set.

4. Option D: "Standard deviation tells us how much the data deviates from the mean of the data."

   • True. This is the correct interpretation of standard deviation. It measures the average amount by which each data point deviates from the mean.

5. Option E: "None of the answer choices are correct."

   • False. Since we identified that options A and D are correct, this option is also incorrect.

Thus, A and D are true statements about standard deviation.

Do you want further details or have any questions?

Here are some follow-up questions:

1. Can you explain how standard deviation is calculated for a data set?
2. What are the key differences between variance and standard deviation?
3. How does the standard deviation change if all data points in a set are equal?
4. In what situations would you prefer using standard deviation over range as a measure of dispersion?
5. How does standard deviation help in understanding the distribution of data?

Tip: When working with data, always pair the mean and standard deviation to get a clearer understanding of the dataset's central tendency and spread.