Timeline for Best estimator of the mean of a normal distribution based only on box-plot statistics
Current License: CC BY-SA 4.0
6 events
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| Jul 25, 2023 at 17:08 | comment | added | Glen_b | @Henry Oh, thanks, yes, it is "sample mean", it says it right there in the title of the paper. I glossed right over that | |
| Jul 25, 2023 at 16:39 | comment | added | Henry | @Glen_b: that was apparently for estimating the sample mean. I read the OP as estimating the population mean, in which case I would have thought $r$ and $q$ would be substantially smaller. | |
| Jul 25, 2023 at 7:05 | comment | added | Glen_b | Looking at the 2018 paper by Shi et al on arxiv "How to estimate the sample mean and standard deviation from the five number summary?" which refers to an earlier version of the Luo paper, they do focus on the normal case (and within that, restrict attention to the case $n\!\mod\!4=1$); they recommend - exactly as I just did in my answer - to use a weighted average of median, midhinge and midrange. Their recommendation is (in my notation) $r = 2.2/(2.2+n^{0.75}), q = 0.7−0.72n^{-0.55}$. Unsure these functions will be quite right at very large $n$, though | |
| Jul 25, 2023 at 6:29 | comment | added | Glen_b | @Jacob do any of those papers proceed under the OP's assumption that the population distribution is normal (the titles don't suggest it). If they do, perhaps you could summarize what they do and what they conclude in an answer. | |
| Jul 25, 2023 at 4:03 | comment | added | Jacob | Shi et al. (2020). "Optimally estimating the sample standard deviation from the five-number summary", Research Synthesis Methods, 11: 641-654. Luo et al. (2018), "Optimally estimating the sample mean from the sample size, median, mid-range and/or mid-quartile range", Statistical Methods in Medical Research, 27: 1785-1805. Want et al., "Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range", BMC Medical Research Methodology, 14: 135. | |
| Jul 25, 2023 at 3:58 | history | answered | kjetil b halvorsen♦ | CC BY-SA 4.0 |