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How is the mean represented in boxplots? In the image below weather situation 3 shows outliers pulling the mean down and so I reasoned that situation 4 would have a higher mean than the rest because the median has a higher Humidity than situation 1 and 2. But, I got the wrong answer. Thank you.

enter image description here

sgoodman
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    The mean is not usually represented in boxplots. That being said, I do not see how the mean of station $4$ can be below $0.81$ (unless something is missing from the picture - half the Station $4$ seem to be almost identical) or the mean of station $1$ be above $0.7$ or the mean of station $2$ be above $0.8$. It is possible that Station $3$ has a higher mean than Station $4$ – Henry Sep 21 '19 at 10:12
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    Usually the 'mean' is presented by a symbol (cross, circle, square). – Nick Sep 21 '19 at 10:17

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Comments by @Henry and @Nick are true and possibly helpful. But they may not tell the whole story here. Normally, boxplots show the sample median (cross-bar inside the box), but not the mean.

Sometimes, you can guess the value of the sample mean, but that can be difficult because (other than outliers) exact positions of only five points at most are shown in a boxplot. However, means can be superimposed upon boxplots, as I have shown below.

Below are boxplots of four samples, each of size $n = 100$ from different beta distributions, with respective population means $2/4 = 0.5,\,$ $3/5 = 0.6,\,$ $11/12 \approx 0.917,$ and $9/10 = 0.9.$ Sample means follow roughly the same pattern.

I contrived these samples to give boxplots that look somewhat like the ones in your question. R code for simulating the samples and making the figure is shown in the Addendum.

enter image description here

As you can see, in spite of the low outliers in Group 3, that group has a slightly higher sample mean than does Group 4. Because you can't know the positions of all the points, I'm not sure how you would know the relative positions of the means---unless I had plotted the means as red $+$-symbols.

In my example, all four groups have the same sample size. Boxplots don't give much information about sample sizes. A boxplot is not intended to give a complete description of the sample. If sample sizes differ, it is even more difficult to compare details of samples that are not represented in a boxplot.

Addendum. If you use R, you can make various different examples, similar to mine, by omitting the set.seed statement in the first line.

set.seed(921)
x1 = rbeta(100, 2, 2);  x2 = rbeta(100, 3, 2)
x3 = rbeta(100, 11, 1);  x4 = rbeta(100, 90, 10)
x = c(x1,x2,x3,x4);  g = rep(1:4, each=100)
MAT = matrix(x,byrow=T,nrow=4)
a = rowMeans(MAT); a
[1] 0.5112790 0.6229495 0.9134846 0.9016410
boxplot(x ~ g, col="skyblue2")
 points(1:4, a, pch="+", col="red")
BruceET
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