Let's compute both the range and the interquartile range (IQR) for the given data values:

Data values:

$10, 20, 11, 16, 17$

Step 1: Arrange the data in ascending order.

$10, 11, 16, 17, 20$

Step 2: Calculate the Range.

The range is the difference between the maximum and minimum values in the dataset. $\text{Range} = \text{Maximum} - \text{Minimum} = 20 - 10 = 10$

Step 3: Calculate the Interquartile Range (IQR).

The IQR is the range between the first quartile (Q1) and the third quartile (Q3).

1. Median (Q2):

Since there are 5 data points, the median is the middle value (the 3rd value). $Q2 = 16$

2. First Quartile (Q1):

Q1 is the median of the lower half of the data (values below the median). The lower half is: $10, 11$ The median of these two values is: $Q1 = \frac{10 + 11}{2} = 10.5$

3. Third Quartile (Q3):

Q3 is the median of the upper half of the data (values above the median). The upper half is: $17, 20$ The median of these two values is: $Q3 = \frac{17 + 20}{2} = 18.5$

4. IQR Calculation:

$\text{IQR} = Q3 - Q1 = 18.5 - 10.5 = 8$

Final Results:

• Range = 10
• Interquartile Range (IQR) = 8

---

Would you like any further details on the calculation process or have any questions about the results?

---

Here are some follow-up questions to explore further:

1. How does the IQR help in detecting outliers in a dataset?
2. What are the steps for calculating quartiles for larger datasets?
3. How would you compute the range and IQR for a dataset with more values?
4. What is the difference between the range and standard deviation as measures of spread?
5. How would the IQR change if we added an extreme outlier to the dataset?

Tip: The IQR is a more robust measure of spread compared to the range, especially when your dataset contains outliers.