Thirteen internists in the Midwest are randomly selected, and each internist is asked to report last year's income. The incomes obtained (in thousands of dollars) are 152, 144, 162, 154, 146, 241, 127, 141, 171, 177, 138, 132, 192.  Find the first quartile

To find the first quartile (Q1) of the given dataset, we follow these steps:

1. **Arrange the data in ascending order**:
   \[
   127, 132, 138, 141, 144, 146, 152, 154, 162, 171, 177, 192, 241
   \]

2. **Find the position of the first quartile (Q1)**:
   The first quartile is the value that divides the lowest 25% of the data. To find its position, we use the formula:
   \[
   Q1 = \frac{n + 1}{4}
   \]
   where \(n\) is the number of data points.

   Here, \(n = 13\), so:
   \[
   Q1 = \frac{13 + 1}{4} = \frac{14}{4} = 3.5
   \]
   This means the first quartile lies between the 3rd and 4th values in the ordered data.

3. **Calculate Q1**:
   The 3rd value in the ordered data is 138, and the 4th value is 141. Since the position of Q1 is 3.5, it is the average of these two values:
   \[
   Q1 = \frac{138 + 141}{2} = \frac{279}{2} = 139.5
   \]

Thus, the first quartile (Q1) is **139.5**.

Would you like more details or have any questions about the calculation? 

Here are 5 related questions:
1. How do you interpret quartiles in a dataset?
2. What is the second quartile (median) of this data?
3. What is the third quartile (Q3) for this dataset?
4. How can quartiles be useful in analyzing income distributions?
5. How does the presence of outliers (like 241) affect quartile calculations?

**Tip**: Quartiles help in dividing data into meaningful segments, providing insights into distribution and spread.

Thirteen internists in the Midwest are randomly selected, and each internist is asked to report last year's income. The incomes obtained (in thousands of dollars) are 152, 144, 162, 154, 146, 241, 127, 141, 171, 177, 138, 132, 192. Find the first quartile.

Learn how to calculate the first quartile (Q1) for a dataset representing the annual income of 13 randomly selected internists in the Midwest. The incomes range from 127 to 241 (in thousands), and the first quartile value is calculated as 139.5. Step-by-step solution included for high school-level statistics.

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