A sample of 25 students' ages were collected at a college. If the following is the 5 number summary for this set of data, find the IQR (Interquartile Range)

**Minimum**

**Q1**

**Median**

**Q3**

**Maximum**

20 years

33 years

42 years

53 years

60 years

IQR of the sample:  years

The Interquartile Range (IQR) is calculated as the difference between the third quartile (Q3) and the first quartile (Q1):

\[
\text{IQR} = Q3 - Q1
\]

Given the five-number summary:

- Q1 = 33 years
- Q3 = 53 years

Thus, the IQR is:

\[
\text{IQR} = 53 - 33 = 20 \text{ years}
\]

The IQR of the sample is **20 years**.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. What does the Interquartile Range (IQR) tell you about the spread of the data?
2. How does the IQR compare to the range of the dataset?
3. Why is the IQR often preferred over the range as a measure of dispersion?
4. How can outliers be identified using the IQR?
5. What does the five-number summary represent in a box plot?

**Tip:** The IQR is a robust measure of spread because it is not affected by outliers, unlike the range.

A sample of 25 students' ages were collected at a college. If the following is the 5 number summary for this set of data, find the IQR (Interquartile Range). Minimum: 20 years, Q1: 33 years, Median: 42 years, Q3: 53 years, Maximum: 60 years.

Learn how to calculate the Interquartile Range (IQR) from a five-number summary. In this example, ages of 25 students are used to demonstrate how to subtract Q1 from Q3. The IQR measures the spread of the middle 50% of the data. Suitable for students in Grades 9-11.

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