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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
attach(my_data)
library("car")
n = length(len)
z = 1.96
stndev = sd(len)
meansample = mean(my_data$len)
mediansample = median(len)
bound = z+(stndev/sqrt(n))
qqPlot(len)
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

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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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