Let's first organize the numbers in ascending order and then calculate the interquartile range (IQR).

Step 1: Sort the numbers

The given numbers are:
10, 15, 25, 19, 37, 62, 29, 8, 6, 30, 15, 20

Arranging them in ascending order:

6, 8, 10, 15, 15, 19, 20, 25, 29, 30, 37, 62

Step 2: Find the median (Q2)

The median divides the data into two halves. Since there are 12 numbers (even), the median is the average of the 6th and 7th numbers.

The 6th number is 19, and the 7th number is 20.

$\text{Median (Q2)} = \frac{19 + 20}{2} = 19.5$

Step 3: Find the lower quartile (Q1)

The lower quartile (Q1) is the median of the lower half of the data, which consists of the first 6 numbers:

6, 8, 10, 15, 15, 19

The median of these is the average of the 3rd and 4th numbers, which are 10 and 15.

$\text{Q1} = \frac{10 + 15}{2} = 12.5$

Step 4: Find the upper quartile (Q3)

The upper quartile (Q3) is the median of the upper half of the data, which consists of the last 6 numbers:

20, 25, 29, 30, 37, 62

The median of these is the average of the 3rd and 4th numbers, which are 29 and 30.

$\text{Q3} = \frac{29 + 30}{2} = 29.5$

Step 5: Calculate the interquartile range (IQR)

The interquartile range (IQR) is the difference between Q3 and Q1.

$\text{IQR} = Q3 - Q1 = 29.5 - 12.5 = 17$

Final Answer:

The Interquartile Range (IQR) is 17.

Would you like a more detailed breakdown of any step? Feel free to ask!

Here are some follow-up questions:

1. How do you calculate the median for an even number of data points?
2. What is the difference between Q1, Q2, and Q3 in terms of data interpretation?
3. How can I use the IQR to detect outliers in a dataset?
4. What happens if you have an odd number of data points instead of even?
5. How is the standard deviation related to the interquartile range?

Tip: The IQR helps you understand the spread of the middle 50% of your data, which can be more robust to outliers than using the range alone.