Suppose, we have 10 observations such that 39, 46, 44, 30, 73, 96, 91, 115, 112, 89. Calculate the Inter Quartile Range (IQR) of the data.

To calculate the Inter Quartile Range (IQR) of the data set, follow these steps:

1. **Sort the data in ascending order:**
   \[
   30, 39, 44, 46, 73, 89, 91, 96, 112, 115
   \]

2. **Find the median (Q2):**
   Since there are 10 observations (an even number), the median is the average of the 5th and 6th numbers in the sorted list.
   \[
   Q2 = \frac{73 + 89}{2} = \frac{162}{2} = 81
   \]

3. **Find the first quartile (Q1):**
   Q1 is the median of the first half of the data (the first 5 numbers).
   \[
   30, 39, 44, 46, 73
   \]
   The median of these 5 numbers is the 3rd number:
   \[
   Q1 = 44
   \]

4. **Find the third quartile (Q3):**
   Q3 is the median of the second half of the data (the last 5 numbers).
   \[
   89, 91, 96, 112, 115
   \]
   The median of these 5 numbers is the 3rd number:
   \[
   Q3 = 96
   \]

5. **Calculate the IQR:**
   \[
   IQR = Q3 - Q1 = 96 - 44 = 52
   \]

So, the Inter Quartile Range (IQR) of the data is 52.

Would you like further details or have any questions?

Here are 5 numbered questions for you to ask next:
1. How do you calculate the standard deviation of a data set?
2. Can you explain the difference between variance and standard deviation?
3. How do you find the mode of a data set?
4. What is the difference between a population and a sample in statistics?
5. How do you perform a hypothesis test for the mean of a population?

Tip: The IQR is a measure of statistical dispersion and is useful for identifying the spread of the middle 50% of a data set, often used to detect outliers.

Learn how to calculate the Inter Quartile Range (IQR) from a given dataset of 10 observations: 39, 46, 44, 30, 73, 96, 91, 115, 112, 89. Follow a detailed step-by-step solution including sorting, finding quartiles, and computing IQR. Suitable for students in Grades 9-12.

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