What is the interquartile range for the following 
12,5,22,30,7,36,14,42,15,53,25,65 

To find the **interquartile range (IQR)**, follow these steps:

1. **Order the data** in ascending order:
   \[
   5, 7, 12, 14, 15, 22, 25, 30, 36, 42, 53, 65
   \]

2. **Find the median** (Q2):
   - There are 12 numbers, so the median is the average of the 6th and 7th numbers.
   \[
   Q2 = \frac{22 + 25}{2} = 23.5
   \]

3. **Find the lower quartile** (Q1):
   - The lower quartile is the median of the lower half (first 6 numbers):
   \[
   5, 7, 12, 14, 15, 22
   \]
   The median of this set is the average of the 3rd and 4th numbers.
   \[
   Q1 = \frac{12 + 14}{2} = 13
   \]

4. **Find the upper quartile** (Q3):
   - The upper quartile is the median of the upper half (last 6 numbers):
   \[
   25, 30, 36, 42, 53, 65
   \]
   The median of this set is the average of the 3rd and 4th numbers.
   \[
   Q3 = \frac{36 + 42}{2} = 39
   \]

5. **Calculate the interquartile range (IQR)**:
   \[
   IQR = Q3 - Q1 = 39 - 13 = 26
   \]

So, the **interquartile range (IQR)** is **26**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you interpret the IQR in terms of data spread?
2. What does a larger IQR indicate about data variability?
3. Can outliers be detected using IQR?
4. How do quartiles help in understanding the distribution of data?
5. How is IQR different from the range?

**Tip:** The IQR is useful because it is not affected by extreme values or outliers, unlike the total range.

What is the interquartile range for the following 12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25, 65?

Learn how to calculate the interquartile range (IQR) for the data set 12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25, 65. This problem covers descriptive statistics concepts like quartiles, median, and the interquartile range. Suitable for students in Grades 9-11.

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