Question: 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?
A The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A.
B The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A.
C The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.
D The median of data set B is greater than the median of data set A, and the range of data set B is greater than the range of data set A.
1. **State the problem:** We have data set A with 15 values shown in a dot plot: 5 values at 22, 4 at 23, 3 at 24, 2 at 25, and 1 at 26.
2. **Find the median of data set A:** Since there are 15 values, the median is the 8th value when ordered.
Counting values in order:
- Values 1 to 5 are 22
- Values 6 to 9 are 23
The 8th value is 23, so the median of data set A is $23$.
3. **Find the range of data set A:** Range is maximum value minus minimum value.
- Minimum value = $22$
- Maximum value = $26$
So, range of data set A is $$26 - 22 = 4$$.
4. **Create data set B by adding 56 to each value in data set A:**
- Median of data set B = median of data set A + 56 = $$23 + 56 = 79$$.
- Minimum value of data set B = $$22 + 56 = 78$$.
- Maximum value of data set B = $$26 + 56 = 82$$.
5. **Find the range of data set B:**
$$82 - 78 = 4$$.
6. **Compare medians and ranges:**
- Median of B ($79$) is greater than median of A ($23$).
- Range of B ($4$) is equal to range of A ($4$).
7. **Conclusion:** The correct choice is C: "The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A."