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The problem asks to compare data set A with data set B, where data set B is created by adding 56 to each value in data set A. We are tasked with identifying the correct comparison of the medians and ranges between the two data sets.

### Step 1: Understand the Impact on Median and Range
- **Median**: Adding a constant value (56) to each data point shifts the entire data set, but it does not change the relative position of the values. Therefore, the median of data set B will be **56 greater** than the median of data set A.
  
- **Range**: The range is the difference between the maximum and minimum values. Since adding a constant to each value in a data set increases both the maximum and minimum by the same amount, the range **remains the same** for data set B as for data set A.

### Step 2: Analyze the Options
Now let's analyze the options based on this understanding:
- **A**: Median of B is equal to median of A, and the range of B is equal to the range of A.  
  - Incorrect, since the median of B is 56 greater than the median of A.
  
- **B**: Median of B is equal to median of A, and the range of B is greater than the range of A.  
  - Incorrect for the same reason as option A (the median is not the same).

- **C**: Median of B is greater than the median of A, and the range of B is equal to the range of A.  
  - Correct! The median of B is 56 greater, but the range remains the same.

- **D**: Median of B is greater than the median of A, and the range of B is greater than the range of A.  
  - Incorrect, because the range does not change.

### Correct Answer: **C**

Would you like further clarification or a breakdown of specific concepts?

### Related Questions:
1. What happens to the mean when a constant is added to each data value?
2. How does multiplying all data values by a constant affect the median and range?
3. How is the interquartile range (IQR) affected when a constant is added to a data set?
4. What is the difference between median and mode in skewed data?
5. How do transformations affect measures of spread like variance or standard deviation?

### Tip:
Always remember that adding a constant to each value in a data set affects the central tendency (like the median) but not the spread (like the range or standard deviation).

The dot plot represents the 15 values in data set A. Data set B is created by adding 56 to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?

In this problem, data set B is formed by adding 56 to each value in data set A. The correct comparison of medians and ranges is analyzed, demonstrating that adding a constant shifts the median but leaves the range unchanged. Learn how transformations affect statistical measures.

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