In the data set below, what is the interquartile range \( \begin{array}{lllll}58 & 70 & 27 & 47 & 92\end{array} \)

To find the interquartile range (IQR) of the data set \( \begin{array}{lllll}58 & 70 & 27 & 47 & 92\end{array} \), first, we need to arrange the numbers in ascending order: \( 27, 47, 58, 70, 92 \). Next, identify the lower quartile (Q1) and upper quartile (Q3). For this five-number set, Q1 is the median of the first half (27, 47), which is 37. Q3 is the median of the second half (58, 70, 92), which is 70. Finally, the IQR is calculated as Q3 - Q1, which gives us 70 - 47 = 23. So, the interquartile range is 23! Another fun fact: The interquartile range is a great tool for identifying outliers in your data. If a value falls outside \( Q1 - 1.5 \times IQR \) or \( Q3 + 1.5 \times IQR \), it’s considered an outlier. This allows you to grasp the spread of your data while not letting a few extreme values skew your results! Moreover, the concept of the IQR is heavily used in box plots. Box plots give you a visual representation of the data distribution using quartiles and can really help in spotting trends and data variation at a quick glance. It’s a simple yet powerful tool in statistical analysis!