Which of the following is a true statement?

Group of answer choices

The sum of the deviations from the mean is 100%

The mean is the balance point for a given set of data.

The mean is a better measure of center for a skewed data distribution.

The Variance is the square root of the median.

The true statement among the options is:

**"The mean is the balance point for a given set of data."**

### Explanation:
- **The sum of the deviations from the mean is 100%:** This statement is incorrect. The sum of the deviations from the mean (i.e., the sum of \((x_i - \bar{x})\) for all data points \(x_i\)) is always **0**, not 100%.
  
- **The mean is the balance point for a given set of dataThe true statement among the options is:

**"The mean is the balance point for a given set of data."**

### Explanation:
- **The sum of the deviations from the mean is 100%:** This statement is incorrect. The sum of the deviations from the mean (i.e., the sum of \((x_i - \bar{x})\) for all data points \(x_i\)) is always **0**, not 100%.
  
- **The mean is the balance point for a given set of ** This statement is correct. The mean is considered the balance point because the sum of the deviations from the mean on one side of the mean is equal in magnitude to the sum of the deviations on the other side.
  
- **The mean is a better measure of center for a skewed data distribution:** This statement is incorrect. For skewed distributions, the **median** is generally a better measure of central tendency because it is less affected by outliers and skewed data.
  
- **The Variance is the square root of the median:** This statement is incorrect. The variance is the average of the squared deviations from the mean, not related to the median in this way. The **standard deviation** is the square root of the variance, not the median.

Would you like more details on any of these concepts or have any further questions?

### Relative Questions:
1. Why is the sum of deviations from the mean always zero?
2. How does the mean act as a balance point in a data set?
3. What are the implications of using the mean in a skewed distribution?
4. How does the median differ from the mean in terms of robustness to outliers?
5. What is the relationship between variance and standard deviation?

### Tip:
For skewed distributions, consider using the median instead of the mean to better represent the central tendency.

Explore the concept of central tendency in statistics with a focus on the mean. Learn why the mean is considered the balance point for a set of data and its implications. Understand why the mean may not always be suitable for skewed distributions.

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