To calculate the interquartile range (IQR) of the given data set, follow these steps:

Data set: 48, 34, 8, 33, 27

Step 1: Arrange the data in ascending order.

8, 27, 33, 34, 48

Step 2: Find the quartiles.

• Median (Q2): The median divides the data set into two halves. Since there are 5 numbers, the middle number is 33. So, Q2 = 33.

• Lower Quartile (Q1): This is the median of the lower half (excluding Q2). The lower half is 8, 27. The median of this subset is (8 + 27)/2 = 17.5.

• Upper Quartile (Q3): This is the median of the upper half (excluding Q2). The upper half is 34, 48. The median of this subset is (34 + 48)/2 = 41.

Step 3: Calculate the interquartile range (IQR).

IQR = Q3 - Q1 = 41 - 17.5 = 23.5

The interquartile range is 23.5.

Would you like more details on this solution?

Here are 5 related questions for further practice:

1. What does the interquartile range represent in a data set?
2. How do you identify outliers using the interquartile range?
3. If a new number, say 50, is added to the data set, how would the interquartile range change?
4. What are other methods to measure data dispersion besides the interquartile range?
5. Can the interquartile range be negative, and why?

Tip: The IQR is resistant to extreme values, making it a robust measure of spread in skewed data.