To find the interquartile range (IQR), follow these steps:

1. Arrange the data in ascending order: $8.7, 9.0, 9.2, 9.5, 9.7, 10.0, 10.0, 10.8$

2. Find the first quartile (Q1): Q1 is the median of the lower half of the data (excluding the overall median if the data set is odd).

   Lower half: $8.7, 9.0, 9.2, 9.5$

   The median of this set (average of 9.0 and 9.2): $Q1 = \frac{9.0 + 9.2}{2} = 9.1$

3. Find the third quartile (Q3): Q3 is the median of the upper half of the data.

   Upper half: $9.7, 10.0, 10.0, 10.8$

   The median of this set (average of 10.0 and 10.0): $Q3 = 10.0$

4. Calculate the interquartile range (IQR): $\text{IQR} = Q3 - Q1 = 10.0 - 9.1 = 0.9$

Thus, the interquartile range (IQR) is 0.9.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

1. What does the interquartile range tell us about data spread?
2. How does IQR help in detecting outliers in a data set?
3. Can you explain the difference between IQR and range?
4. How can the quartiles be visually represented on a box plot?
5. How would the IQR change if an additional data point were added?

Tip: IQR is a robust measure of variability, less affected by outliers compared to range.