The Interquartile Range (IQR) is a measure of statistical dispersion, or how spread out the values in a data set are. It specifically represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset.

Steps to find the Interquartile Range:

1. Arrange the data in ascending order.

2. Find the median (Q2):

   • If the number of data points is odd, the median is the middle value.
   • If the number of data points is even, the median is the average of the two middle values.

3. Find Q1 (the first quartile):

   • This is the median of the lower half of the data, excluding the overall median if the number of data points is odd.
   • It divides the lower half of the data set into two equal parts.

4. Find Q3 (the third quartile):

   • This is the median of the upper half of the data, excluding the overall median if the number of data points is odd.
   • It divides the upper half of the data set into two equal parts.

5. Calculate the IQR: $IQR = Q3 - Q1$

Example:

Consider the dataset:
$2, 4, 7, 10, 12, 15, 18, 22, 25, 30$

1. Sort the data: It's already sorted. $2, 4, 7, 10, 12, 15, 18, 22, 25, 30$

2. Find the median (Q2):
   Since there are 10 data points (even), the median is the average of the 5th and 6th values.
   $Q2 = \frac{12 + 15}{2} = 13.5$

3. Find Q1 (median of the lower half: 2, 4, 7, 10, 12): $Q1 = 7 \quad (\text{middle value of the lower half})$

4. Find Q3 (median of the upper half: 15, 18, 22, 25, 30): $Q3 = 22 \quad (\text{middle value of the upper half})$

5. Calculate the IQR: $IQR = Q3 - Q1 = 22 - 7 = 15$

Thus, the Interquartile Range (IQR) is 15.

Summary Formula:

$IQR = Q3 - Q1$

Would you like more clarification on any of these steps, or do you have a specific data set you'd like to calculate the IQR for?

Related questions:

1. How do you calculate quartiles for an odd or even number of data points?
2. What does the IQR tell us about the spread of data?
3. How do you use the IQR to identify outliers in a dataset?
4. How is the IQR related to the standard deviation?
5. How do you interpret the IQR in the context of box plots?

Tip:

The IQR is especially useful for identifying outliers because any data point that lies more than 1.5 times the IQR above Q3 or below Q1 is typically considered an outlier.