What is the interquartile range of 10, 12, 14, 16, 18, 20, 22?

The interquartile range (IQR) of 10, 12, 14, 16, 18, 20, 22 is 8.

To find the interquartile range, we first need to identify the lower quartile (Q1) and the upper quartile (Q3). The interquartile range is the difference between these two values. The lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half.

First, let's find the median of the entire dataset. The dataset is already in ascending order: 10, 12, 14, 16, 18, 20, 22. Since there are 7 numbers, the median is the fourth number, which is 16.

Next, we find the lower quartile (Q1). This is the median of the lower half of the data: 10, 12, 14. The median of these three numbers is 12.

Then, we find the upper quartile (Q3). This is the median of the upper half of the data: 18, 20, 22. The median of these three numbers is 20.

Finally, we calculate the interquartile range by subtracting the lower quartile from the upper quartile: IQR = Q3 - Q1 = 20 - 12 = 8.

So, the interquartile range of the dataset 10, 12, 14, 16, 18, 20, 22 is 8. The IQR is a measure of the spread of the middle 50% of the data, helping to understand the variability without being affected by extreme values.