1. **Stating the problem:** We have data set A with 15 values: 5 values of 22, 4 values of 23, 3 values of 24, 2 values of 25, and 1 value of 26. Data set B is created by adding 46 to each value in data set A. We need to compare the medians and ranges of data sets A and B. 2. **Recall definitions:** - The **median** is the middle value when data is ordered. - The **range** is the difference between the maximum and minimum values. 3. **Find the median of data set A:** - Since there are 15 values, the median is the 8th value when ordered. - Counting from smallest to largest: - 5 values of 22 (positions 1 to 5) - 4 values of 23 (positions 6 to 9) - The 8th value is within the 23s, so median of A is $23$. 4. **Find the range of data set A:** - Minimum value is $22$. - Maximum value is $26$. - Range of A is $$26 - 22 = 4$$. 5. **Create data set B by adding 46 to each value:** - Minimum value of B is $22 + 46 = 68$. - Maximum value of B is $26 + 46 = 72$. 6. **Find the median of data set B:** - Adding a constant to all values shifts the median by that constant. - Median of B is $$23 + 46 = 69$$. 7. **Find the range of data set B:** - Range of B is $$72 - 68 = 4$$. 8. **Compare medians and ranges:** - Median of B ($69$) is greater than median of A ($23$). - Range of B ($4$) is equal to range of A ($4$). **Final answer:** a. 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