What are some examples of the IQR method in statistics?

Can you explain the IQR method and provide some examples?

Sure! The IQR, or Interquartile Range, is a measure of statistical dispersion. It represents the range between the first quartile (Q1) and the third quartile (Q3). For example, if you have a dataset of test scores: [55, 60, 65, 70, 75, 80, 85, 90], Q1 is 65 and Q3 is 80, so the IQR is 80 - 65 = 15.

How do you calculate Q1 and Q3?

To calculate Q1 and Q3, you first need to sort your data. Then, Q1 is the median of the first half of the data, and Q3 is the median of the second half. For the dataset [55, 60, 65, 70, 75, 80, 85, 90], Q1 is the average of 60 and 65, which is 62.5, and Q3 is the average of 80 and 85, which is 82.5.

Can you give me another example with a larger dataset?

Absolutely! Consider the dataset: [10, 12, 14, 15, 18, 20, 22, 25, 30, 35]. After sorting, Q1 is 15 and Q3 is 22. Thus, the IQR is 22 - 15 = 7.

What does a high IQR indicate about a dataset?

A high IQR indicates that there is a wide spread between the middle 50% of the data points, suggesting greater variability in the dataset.