**Populations For a recent year, the data in millions show the population of ten large cities in the United States. Find the first and third quartiles and the IQR.**

**9.2**

**2.2**

**2.6**

**1.7**

**1.2**

**3.8**

**1.4**

**1.5**

**1.6**

**2.0**

**The first quartile Q3 is**

To find the first and third quartiles and the interquartile range (IQR), we follow these steps:

1. **Order the data from smallest to largest:**
   \[
   1.2, 1.4, 1.5, 1.6, 1.7, 2.0, 2.2, 2.6, 3.8, 9.2
   \]

2. **First Quartile (Q1):**
   The first quartile \(Q_1\) is the median of the lower half of the data (excluding the median if the dataset has an odd number of observations). 
   
   Here, we have 10 data points, so the lower half consists of the first 5 points: 
   \[
   1.2, 1.4, 1.5, 1.6, 1.7
   \]
   The median of these values is \( Q_1 = 1.5 \).

3. **Third Quartile (Q3):**
   The third quartile \(Q_3\) is the median of the upper half of the data. The upper half is:
   \[
   2.0, 2.2, 2.6, 3.8, 9.2
   \]
   The median of these values is \( Q_3 = 2.6 \).

4. **Interquartile Range (IQR):**
   The IQR is calculated as the difference between the third and first quartiles:
   \[
   IQR = Q_3 - Q_1 = 2.6 - 1.5 = 1.1
   \]

### Summary:
- **First Quartile (Q1):** 1.5
- **Third Quartile (Q3):** 2.6
- **Interquartile Range (IQR):** 1.1

Would you like any more details or have any questions about this process?

Here are 5 related questions:
1. What is the median of the dataset?
2. How is the interquartile range (IQR) useful in data analysis?
3. Can you explain what outliers are and how they relate to the IQR?
4. How do quartiles divide a dataset?
5. What would the second quartile (Q2) represent in this context?

**Tip:** The interquartile range is useful for detecting outliers, as any value more than 1.5 times the IQR from the quartiles is considered an outlier.

Populations For a recent year, the data in millions show the population of ten large cities in the United States. Find the first and third quartiles and the IQR.

9.2

2.2

2.6

1.7

1.2

3.8

1.4

1.5

1.6

2.0

The first quartile Q3 is

Learn how to find the first and third quartiles (Q1 and Q3) and calculate the interquartile range (IQR) using population data from ten large US cities. Follow a step-by-step guide to understand key statistical concepts like quartiles and IQR. Suitable for students in Grades 9-12.

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