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The problem asks for the correct interpretation of the standard deviation given a dotplot and some statistical information.

The dotplot shows the fat content (in grams) for 12 different hamburgers. It is stated that the mean fat content \( \mu \) is 22.83 grams, and the standard deviation \( \sigma_x \) is 9.06 grams.

Let's evaluate the provided choices:

1. **"The fat content of these 12 hamburgers typically varies by about 9.06 grams from the mean of 22.83 grams."**
   - This is a correct interpretation of the standard deviation. Standard deviation measures the typical amount by which individual data points deviate from the mean. So, this statement accurately reflects that the fat content typically varies by around 9.06 grams from the mean.

2. **"Standard deviation is calculated by finding the sum of the squared differences of each individual value and the mean. Then, you divide by the sample size minus one. Finally, take the square root."**
   - This is a correct description of how to calculate the standard deviation, but it's more of a technical description of the process rather than an interpretation of what the standard deviation represents in this context. 

3. **"Mean and standard deviation are the correct measures of center and variability to report for this distribution because the dotplot is fairly symmetric. There is a lot of variability in the fat content of the hamburgers from this restaurant."**
   - While this statement makes sense in a general context (mean and standard deviation are good measures for symmetric distributions), it doesn't directly address the standard deviation of 9.06 grams.

4. **"You can expect the fat content of these 12 burgers to vary from 13.77 to 31.89 grams."**
   - This statement refers to a range based on one standard deviation above and below the mean (22.83 ± 9.06). Although this is numerically correct, it’s not a standard interpretation of what standard deviation represents.

### Conclusion:
The best answer is **the first option**: "The fat content of these 12 hamburgers typically varies by about 9.06 grams from the mean of 22.83 grams."

Would you like to dive deeper into any particular concept or have further questions?

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### 5 Related Questions:
1. How would you interpret the mean in the context of this hamburger fat content data?
2. What does it mean if the standard deviation were much smaller than 9.06 grams?
3. How would the interpretation change if the distribution were skewed instead of symmetric?
4. What does it indicate about the dataset if the standard deviation is larger than the mean?
5. How would removing an outlier affect the mean and standard deviation?

### Tip:
When analyzing distributions, always check the shape of the data (e.g., symmetric, skewed) to determine the most appropriate measures of center and spread.

Choose the correct interpretation of the standard deviation from a set of data related to the fat content of 12 hamburgers. The data shows a mean of 22.83 grams and a standard deviation of 9.06 grams.

Learn how to interpret the standard deviation in the context of the fat content of 12 hamburgers. The mean fat content is 22.83 grams, and the standard deviation is 9.06 grams, providing insights into data variability and distribution.

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