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The question is about comparing the standard deviation of scores in the three sections (A, B, and C) shown in the dot plots. Here's how to analyze and solve it:

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### **Step 1: Understanding Standard Deviation**
- **Definition**: Standard deviation measures how spread out the data is around the mean. If most of the data points are close to the mean, the standard deviation will be small. If the data points are more spread out, the standard deviation will be larger.
- **Key Idea**: Since the average score is the same across sections, the spread of data determines the standard deviation.

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### **Step 2: Observing the Dot Plots**
1. **Section A**:
   - Scores are clustered tightly around the mean (mostly between 4 and 6).
   - **Small spread**, so standard deviation is smallest.

2. **Section B**:
   - Scores are moderately spread out (ranging from 0 to 10).
   - Spread is greater than in Section A but less than in Section C.
   - **Intermediate standard deviation**.

3. **Section C**:
   - Scores are the most spread out across the range (from 0 to 10) with gaps in between.
   - **Largest spread**, so standard deviation is highest.

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### **Step 3: Comparing the Standard Deviations**
The standard deviation comparison is as follows:
\[
\text{x (A) < x (B) < x (C)}
\]

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### **Final Answer**:
The standard deviation of scores is smallest for Section A, intermediate for Section B, and largest for Section C.

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Would you like further explanation on standard deviation, the reasoning process, or how to calculate it explicitly?

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### **Related Questions**:
1. What is the mathematical formula for calculating standard deviation?
2. Why is the mean alone insufficient to describe the distribution of data?
3. How does a dot plot help visualize the spread of data?
4. Can two datasets have the same mean but different standard deviations? Why?
5. What are other ways to measure the spread of a dataset besides standard deviation?

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### **Tip**:
When comparing distributions, always look at both the center (mean/median) and spread (standard deviation, range, or interquartile range) for a complete picture.

The dot plots above show the scores on a common quiz for the three sections A, B, and C. Knowing that the average score is the same for the three sections, which of the following correctly compares the standard deviation (x) of the scores in each of the three sections?

Analyze and compare the standard deviations of scores for three sections based on dot plots. Understand how data spread affects standard deviation and learn the reasoning behind the comparisons. Includes a detailed explanation suitable for high school statistics students.

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