April 3 2025 Interquartile Range and Median Concepts

Front

What is the interquartile range (IQR)?

Back

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

Front

How do you find the median of a data set?

Back

To find the median, arrange the data in ascending order and locate the middle value. If there is an even number of observations, the median is the average of the two middle values.

Front

What is a quartile?

Back

A quartile is a type of quantile that divides a ranked data set into four equal parts, with each part containing 25% of the data.

Front

What is the first step in calculating the IQR?

Back

The first step is to put the list of numbers in order from smallest to largest.

Front

What does Q1 represent in a data set?

Back

Q1, or the first quartile, represents the median of the lower half of the data set, effectively marking the 25th percentile.

Front

What does Q3 represent in a data set?

Back

Q3, or the third quartile, represents the median of the upper half of the data set, effectively marking the 75th percentile.

Front

How do you calculate the IQR?

Back

To calculate the IQR, subtract Q1 from Q3: IQR = Q3 - Q1.

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 insight into the variability and potential outliers.

Front

True or False: The IQR can be affected by extreme values in the data set.

Back

False. The IQR is resistant to extreme values because it only considers the middle 50% of the data.

Front

What is the median of the data set: 3, 5, 6, 6, 7, 8, 9?

Back

The median is 6, as it is the middle value of the ordered data set.