What is the third quartile of this data set? \( 14,18,20,21,25,32,42,46,48 \) A. 32 B. 43 C. 42 D. 44

To find the third quartile (Q3) of the data set, we first need to order the numbers (which they already are) and identify the position of Q3. Q3 is the 75th percentile, which can be calculated as \( \frac{3(n+1)}{4} \), where \( n \) is the number of data points. Here, \( n = 9 \), so \( \frac{3(9+1)}{4} = 7.5 \). This means Q3 lies between the 7th and 8th values, which are 42 and 46. Therefore, Q3 is \( \frac{42 + 46}{2} = 44 \). So, the correct answer is D. 44. Using box plots can really help visualize quartiles in a dataset! Imagine drawing a box from the first quartile to the third quartile, with a line at the median. It’s not only a powerful way to summarize data distributions but also gives you a glance at any potential outliers. So next time you’re grappling with numbers, don’t forget to sketch it out—your future self will thank you! If you're curious about more intricate details on quartiles, diving into statistics can be super rewarding! Check out books like "Statistics for Dummies" or "The Art of Statistics" by David Spiegelhalter. They break down concepts like variance, distribution, and quartiles with down-to-earth language and engaging examples. Perfect for anyone looking to brush up on their stats skills while having fun!