Let's go through each option carefully:

• A. Values close together have a small standard deviation
  True. Standard deviation measures how spread out the values are in a data set. If the values are close together, the standard deviation is small because the data points are near the mean.

• B. Measures the variation among one data value from the mean
  False. Standard deviation does not measure the variation of a single data value from the mean. It measures the variation of all data values in the set from the mean, on average.

• C. Measures the variation among all data values from the mean
  True. This is the correct definition of standard deviation. It measures the average deviation of all data points from the mean.

• D. The formulas for population standard deviation and sample standard deviation are the same
  False. The formulas for population standard deviation and sample standard deviation are slightly different. In the sample formula, you divide by $n-1$ (degrees of freedom), while in the population formula, you divide by $n$.

• E. Values further apart have a larger standard deviation
  True. When data points are farther apart from the mean, the standard deviation increases because the data points are more spread out.

• F. Variance is the square root of standard deviation
  False. The variance is actually the square of the standard deviation, not the other way around.

Correct Answers:

A, C, E

---

Would you like more detailed explanations or examples?

Here are some related questions to help you dive deeper into the topic:

1. How do you calculate the sample and population standard deviations?
2. What does the variance tell you about a data set?
3. Can you explain why we use $n-1$ for the sample standard deviation?
4. How would a standard deviation of zero impact a data set?
5. What is the relationship between standard deviation and normal distribution?

Tip: When interpreting standard deviation, remember that a large value means the data points are widely spread out, while a small value indicates that the data points are close to the mean.