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).