To find the interquartile range (IQR) of a dataset, we need to determine the values of the first quartile (Q1) and third quartile (Q3) and calculate their difference.

Steps:

1. Order the Data: Arrange the data in ascending order.

   Ordered dataTo find the interquartile range (IQR) of a dataset, we need to determine the values of the first quartile (Q1) and third quartile (Q3) and calculate their difference.

Steps:

1. Order the Data: Arrange the data in ascending order.

   Ordered $6, 9, 11, 12, 12, 15, 16, 18, 24, 27, 27, 29, 30, 31, 32, 33, 35, 40, 40, 46$

2. Find Q1 and Q3:

   • Since there are 20 values, we can find $Q1$ and $Q3$ by dividing the data into quarters.
   • Q1 is the median of the lower half (the first 10 values).
   • Q3 is the median of the upper half (the last 10 values).

   Lower half (first 10 values): $6, 9, 11, 12, 12, 15, 16, 18, 24, 27$

   $Q1 = \frac{12 + 15}{2} = 13.5$

   Upper half (last 10 values): $27, 29, 30, 31, 32, 33, 35, 40, 40, 46$

   $Q3 = \frac{32 + 33}{2} = 32.5$

3. Calculate the IQR: $\text{IQR} = Q3 - Q1 = 32.5 - 13.5 = 19$

Conclusion

The interquartile range (IQR) is 19 months.

Would you like a more detailed explanation or have any questions?

Here are some related questions to explore further:

1. How is the median different from the interquartile range?
2. What does the IQR tell us about data spread?
3. How does the presence of outliers affect the IQR?
4. What are the benefits of using IQR over range?
5. How do you interpret an IQR in the context of job retention?

Tip: The IQR is a robust measure of variability because it is less sensitive to extreme values than the range.