IQR

Front

What is the definition of the Interquartile Range (IQR)?

Back

The Interquartile Range (IQR) is a measure of statistical dispersion, calculated as the difference between the third quartile (Q3) and the first quartile (Q1). It represents the range of the middle 50% of the data.

Front

How do you calculate the IQR from a data set?

Back

To calculate the IQR, first find Q1 (the median of the lower half of the data), Q2 (the median of the data set), and Q3 (the median of the upper half of the data). Then, subtract Q1 from Q3: IQR = Q3 - Q1.

Front

What is the formula for finding the range of a data set?

Back

The range of a data set is calculated by subtracting the smallest value from the largest value: Range = Maximum value - Minimum value.

Front

What are quartiles in a data set?

Back

Quartiles are values that divide a data set into four equal parts. Q1 is the first quartile (25th percentile), Q2 is the median (50th percentile), and Q3 is the third quartile (75th percentile).

Front

How do you find Q1 in a data set?

Back

To find Q1, arrange the data in ascending order and locate the median of the lower half of the data set (excluding the median if the number of data points is odd).

Front

How do you find Q3 in a data set?

Back

To find Q3, arrange the data in ascending order and locate the median of the upper half of the data set (excluding the median if the number of data points is odd).

Front

What is the significance of the IQR in statistics?

Back

The IQR is significant because it measures the spread of the middle 50% of the data, providing a robust measure of variability that is less affected by outliers compared to the range.

Front

What does a larger IQR indicate about a data set?

Back

A larger IQR indicates greater variability or spread in the middle 50% of the data, suggesting that the data points are more dispersed.

Front

What does a smaller IQR indicate about a data set?

Back

A smaller IQR indicates less variability or spread in the middle 50% of the data, suggesting that the data points are closer together.

Front

How can outliers affect the IQR?

Back

Outliers do not affect the IQR directly because it is based on the quartiles, which are determined by the middle 50% of the data. However, they can affect the overall interpretation of the data.