I’m playing with this little list and my brain is doing that excited-but-confused humming thing: 4, 5, 5, 7, 9, 10, 12, 13, 18, 25.
Range feels obvious (max minus min), but I keep second-guessing myself because that 25 looks a bit outlier-ish. If a question just says “find the range,” do I report the plain max–min no matter what, or is it fair game to mention a trimmed range? I don’t want to overthink it… and yet here I am, overthinking it.
For IQR, I’m stuck in the quartile-definition rabbit hole. With an even number of data points, do I include the middle two numbers when I split into lower and upper halves, or exclude them? And should I be doing any interpolation here, or just take medians-of-halves? My calculator and my spreadsheet don’t agree, which is making my pattern-loving brain twitch.
Follow-up: if I duplicated the largest value (say there were two 25s), would Q3 predictably shift, or does that totally depend on which quartile rule I’m using?
How would you compute the range and IQR for this exact list, and which quartile method would you use on a test if the instructions are vague?
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3 Responses
Range is 25−4=21 (I’d report plain max–min unless told otherwise), and for IQR I’d use Tukey’s “median-of-halves” for even n-exclude the two middle values-so Q1=5 (from 4,5,5,7,9), Q3=13 (from 10,12,13,18,25), IQR=8, though some software’s interpolation will spit out 7.25 or 9.25 instead. If you duplicate 25 then, under Tukey, Q3 jumps to 18 (so IQR grows), but different quartile rules move it differently, so on a test I’d pick the course’s convention-usually Tukey-and say which rule I used; I’m pretty sure that’s what they want.
Range means max–min, so report 25−4=21 (trimmed ranges are only used if the question asks).
For IQR on a test I’d use Tukey’s median-of-halves with no interpolation: split 4,5,5,7,9 | 10,12,13,18,25 so Q1=5, Q3=13, IQR=8; if you duplicate 25 then the upper half is 12,13,18,25,25 so Q3=18 (software that interpolates will give different quartiles).
I think I’d actually toss that outlier-ish 25 and report a trimmed range 18−5=13, and for IQR I’d split including the two middle numbers, average inside each half to get Q1≈7 and Q3≈18 so IQR≈11 (but my spreadsheet grumbles), and if you duplicated 25 I’m pretty sure Q3 would jump to 25. Like packing a picnic: I quietly ditch the bruised apple first, then peek at the middle snacks.