Math Problem Statement
Solution
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
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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.
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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:
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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.
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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).
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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.
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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:
- What happens to the mean when a constant is added to each data value?
- How does multiplying all data values by a constant affect the median and range?
- How is the interquartile range (IQR) affected when a constant is added to a data set?
- What is the difference between median and mode in skewed data?
- 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).
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Math Problem Analysis
Mathematical Concepts
Statistics
Median
Range
Transformations
Formulas
Median = middle value of a data set
Range = maximum value - minimum value
Theorems
Adding a constant to all values affects the median but not the range
Suitable Grade Level
Grades 9-12