I wrote the following code in R to make the following qqplot. In a question I am asked to read the mean and standard deviation of the sample off the plot. I see that the mean can be read as the intersection of the blue line with the vertical line starting from the 0 on the x-axis. However I don't see an obvious way of reading the standard deviation which I tried to draw in brown with the following equation

$$ \mathbf{CI} = \Big[\bar{x}_n \pm Z \cdot \frac{s_x}{\sqrt{n}}\Big] $$

my_data <- ToothGrowth
n = length(len)
z = 1.96
stndev = sd(len)
meansample = mean(my_data$len)
mediansample = median(len)
bound = z+(stndev/sqrt(n))
abline(h=meansample, col="green")
abline(h=mediansample, col="red")
abline(h=meansample+bound, col="brown")
abline(h=meansample-bound, col="brown")

enter image description here


On your plot, standard deviation corresponds to the slope of the center blue line. Remember "rise over run?" If you move left one standard deviation, say from x=0 to x=1, then y increases from about 19 to 27 which is a rise of about roughly 8. Therefore the standard deviation is approximately 8. You can compare this to sd(len).


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