A random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the IQR of the data set.
20	26	30	33
35	35	38	40
41	50	55	57

Give the random variable. (Appropriate rounding rules still apply.)
r.v. =

The random variable (r.v.) in this case refers to the Interquartile Range (IQR) of the data set. To calculate the IQR, we need to follow these steps:

### Step 1: Arrange the data in increasing order (which is already done):
\[ 20, 26, 30, 33, 35, 35, 38, 40, 41, 50, 55, 57 \]

### Step 2: Find the 1st quartile (Q1) and 3rd quartile (Q3):
- **Q1** is the median of the lower half of the data (the first 6 values):
\[ 20, 26, 30, 33, 35, 35 \]
Since there are 6 data points, Q1 is the average of the 3rd and 4th values:
\[
Q1 = \frac{30 + 33}{2} = 31.5
\]

- **Q3** is the median of the upper half of the data (the last 6 values):
\[ 38, 40, 41, 50, 55, 57 \]
Since there are 6 data points, Q3 is the average of the 3rd and 4th values:
\[
Q3 = \frac{41 + 50}{2} = 45.5
\]

### Step 3: Calculate the IQR:
\[
\text{IQR} = Q3 - Q1 = 45.5 - 31.5 = 14
\]

Thus, the random variable (r.v.) is:
\[
\boxed{14}
\]

Would you like more details on this, or do you have any further questions?

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Here are some related questions:
1. How is the median calculated for an odd or even number of data points?
2. What is the significance of the interquartile range in statistics?
3. How can IQR be used to detect outliers in a data set?
4. What are some other measures of variability besides the IQR?
5. How does the IQR differ in skewed vs. normal distributions?

**Tip**: The IQR is resistant to extreme values, making it a robust measure of spread.

A random experiment involves drawing a sample of 12 data values from a normally distributed population. The random variable is the IQR of the data set. 20 26 30 33 35 35 38 40 41 50 55 57. Give the random variable. (Appropriate rounding rules still apply.) r.v. =

Learn how to calculate the Interquartile Range (IQR) of a sample data set drawn from a normally distributed population. Follow step-by-step instructions to find the 1st quartile (Q1), the 3rd quartile (Q3), and compute the IQR. Understand the importance of the IQR in descriptive statistics and its application in data analysis. Suitable for students in Grades 9-12.

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