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If the batches differ in complexity then assigning complex batches to high performers is guaranteed to make them do worse. So unless you're accounting for the different difficulty of batches when comp …

A boxplot is not badly affected by such contamination, but something that put full weight on the most discrepant points would be. …

That's what R does, for example: There are many variations on the box plot, and some packages implement other things than the Tukey boxplot, but it's the most common one. … : (the Crowe version is slightly tweaked here in a couple of ways, one of which makes it seem a bit more boxplot-like; I may do a more faithful version later) …

Here's a basic summary of what's there: All the distributions appear left-skew, "jammed up" against the upper bound of 1.0, with many low 'outliers' tailing off toward the bottom. The 5th category i …

You just calculated the limits on where the whiskers can go, not the whisker ends themselves (which are limited to the range of the data). The actual whiskers go out to the furthest-out data value i …

Since you have the sample means and your hypothesis relates to population means, I've assumed you'll definitely want to use the sample means in what follows. With some distributional assumptions, you …

We can then plot the resulting boxplot. This could work with almost any size of data set as long as you can count the number of observations in a bin. … that default boxplot code to incorporate working through the data portions in lieu of the call to boxplot.stats) …

Short answer - yes, they have a statistical basis. The choice of the basic form of rule (difference between medians as a proportion of overall visual spread) is based on trying to find a simple rule t …

(This section addresses the original question) If we were looking for some relatively formal test, then speaking in general, if there's plenty of points outside the whisker ends, you could maybe get …

When looking at the labelling I would gather that the "median" year is what is being captured by the boxplot. … That's correct, that's what is being displayed by the median line -- but not only the median, since the boxplot includes other information. But that doesn't make much sense in this context. …

(If you need the boxplot anyway, it can't hurt to show the values as well.) … by plotting the quantile plot under the boxplot. …

In R I've done the boxplot and plotted the individual points so you can see what it's doing: > x<-c(16.5, 17.14, 13.5, 16.75) > boxplot(x,boxwex=.2) > points(x~rep(1,4),pch="x",col=2) As you see, … You need to check how they've defined the boxplot (definitions vary - but I think they're not using Tukey's definition of how hinges or whiskers work). …

One option I have seen used which avoids confusion with boxplots (assuming you have medians or original data available) is to plot a boxplot and add a symbol that marks the mean (hopefully with a legend … See also this SO post and this one If you don't have (or really don't want to show) the median a new plot will be needed and then it would be good for it to be visually distinct from a boxplot. …

However, a warning on just how crude the boxplot is. … If we exclude the points marked as boxplot-outliers in that case, we're excluding the point that's telling us that it is actually skew! …

If you're talking about something like this: $\qquad^{\text{[Data are } \tt{1.4, 1.5, 1.7, 1.8, 2.1,2.9, 15 } \text{ ]}}$ then there's probably no real need to remove anything; the display adequate …