The dot plots represent the cost of first-year college tuitions for two different U.S. regions. Which of the statements are true?




I.	Region 1 has a greater mean than region 2.
II.	Region 2 has a greater median than region 1.
III.	Region 1 has a greater interquartile range than region 2.
IV.	Region 2 has a greater standard deviation than region 1.


 A. 
II and IV
 B. 
I and III
 C. 
I and II
 D. 
III and IV

To determine which statements are true, let's break down what each statement implies and how it relates to the dot plots for the two regions.

### Statements:
1. **Statement I: "Region 1 has a greater mean than Region 2."**
   - To verify this, we would compare the average (mean) of the tuition costs for both regions. The mean is sensitive to all values in the data set.
  
2. **Statement II: "Region 2 has a greater median than Region 1."**
   - The median is the middle value when the data points are ordered from least to greatest. Comparing the medians involves looking at the middle of the distributions.

3. **Statement III: "Region 1 has a greater interquartile range (IQR) than Region 2."**
   - The IQR is the range between the first quartile (Q1) and the third quartile (Q3) and measures the spread of the middle 50% of the data. To check this, we would compare the spread of the middle 50% of the data points.

4. **Statement IV: "Region 2 has a greater standard deviation than Region 1."**
   - Standard deviation measures the average distance of each data point from the mean, indicating how spread out the values are. A greater standard deviation means the data is more spread out around the mean.

### Analysis:
- **Statement I:** If Region 1's dot plot has values that are generally higher compared to Region 2, the mean for Region 1 will be greater.
- **Statement II:** If the center of Region 2's dot plot (the median) is higher than the center of Region 1's dot plot, this statement is true.
- **Statement III:** If Region 1 has more variability in the middle 50% of its values compared to Region 2, its IQR would be greater.
- **Statement IV:** If Region 2 has values that are more spread out from the mean than Region 1, its standard deviation will be greater.

### Conclusion:
Without the actual dot plots, the statements can be logically analyzed but not confirmed with certainty. However, typically, in such problems:

- **I** and **III** might correlate because a greater mean might often accompany a greater range, though not always.
- **II** and **IV** might also correlate because a higher median in one region might correspond to a greater spread, increasing the standard deviation.

Given this reasoning:

- If Region 1 indeed has a higher mean, it might also have a greater IQR, making **I and III** true.
- If Region 2 has a higher median, it might have a greater spread (higher standard deviation), making **II and IV** true.

### Answer:
Since the correct answer depends on the data, the most logical option given typical data patterns is **A. II and IV**.

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Would you like more detailed reasoning or explanation? Here are some related questions:

1. How do you calculate the mean and median from a dot plot?
2. What is the relationship between standard deviation and data spread?
3. How do interquartile range and standard deviation differ?
4. What are the steps to find the interquartile range (IQR) in a data set?
5. Why might a higher median correspond to a higher standard deviation?

**Tip:** When comparing distributions, always start by looking at the center (median) and spread (IQR, standard deviation) before diving into specific measures like the mean.

The dot plots represent the cost of first-year college tuitions for two different U.S. regions. Which of the statements are true? I. Region 1 has a greater mean than region 2. II. Region 2 has a greater median than region 1. III. Region 1 has a greater interquartile range than region 2. IV. Region 2 has a greater standard deviation than region 1.

Explore how to analyze dot plots representing first-year college tuitions for two U.S. regions. Learn to compare mean, median, interquartile range (IQR), and standard deviation to determine which statements are true. Suitable for students in Grades 9-12.

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