Let's calculate the median and the range for the given data set: 37, 17, 42, 48, 22, 32, 45, 32.

Step 1: Arrange the data in ascending order

First, we need to sort the data values from smallest to largest: $17, 22, 32, 32, 37, 42, 45, 48$

Step 2: Find the median

The median is the middle value in a data set. Since there are 8 values (an even number), the median will be the average of the 4th and 5th values in the sorted list.

The 4th and 5th values are 32 and 37, respectively.

To find the median: $\text{Median} = \frac{32 + 37}{2} = \frac{69}{2} = 34.5$

Step 3: Calculate the range

The range is the difference between the maximum and minimum values in the data set.

$\text{Range} = \text{Maximum value} - \text{Minimum value} = 48 - 17 = 31$

Final Answers:

• Median: $34.5$
• Range: $31$

Would you like to explore these calculations further, or do you have any other questions? Here are 5 related questions that might be of interest:

1. How would the median change if an additional value, say 50, is added to the data set?
2. What is the mean (average) of the data set?
3. How would you calculate the mode of this data set?
4. If the smallest value (17) were removed, what would the new range be?
5. How would the range change if the largest value were increased to 55?

Tip: When finding the median for an even number of data points, always average the two middle numbers.