Why is the Tukey's IQR not used in the R program? I was writing an R Markdown for calculating measures of spread and was surprised to find that the IQR function does not use the IQR calculation I am used to using, which is:
$$
\text{IQR} = \text{Q3} - \text{Q1}
$$
So with a vector like this:
$$
x = \begin{bmatrix} 10,33,50,341,987,2006,2008 \end{bmatrix}
$$
Q3 should be $2006$ and Q1 should be $33$. Therefore:
$$
\text{IQR} = 2006 - 33 = 1973
$$
However, when running this in R, this does not appear to be how it is derived in the software.
x7 <- c(10,33,50,341,987,2006,2008)
IQR(x7)

Which returns this:
[1] 1455

Looking through the help page, it gives this brief explanation:

Note that this function computes the quartiles using the quantile
function rather than following Tukey's recommendations, i.e., IQR(x) =
quantile(x, 3/4) - quantile(x, 1/4).
For normally N(m,1)N(m,1) distributed XX, the expected value of IQR(X)
is 2*qnorm(3/4) = 1.3490, i.e., for a normal-consistent estimate of
the standard deviation, use IQR(x) / 1.349.

My question is: why would this method be the preferred default if a lot of data is not normally distributed?

Appropriate methods for computing quantiles are a deep rabbit hole. quantile() provides 9 separate methods for computing the quantile; of these 9, 4/9 give the result of 33 that you're expecting:
sapply(1:9, \(t) quantile(x, 0.25, type = t)) |> setNames(1:9)
       1        2        3        4        5        6        7        8 
33.00000 33.00000 33.00000 27.25000 37.25000 33.00000 41.50000 35.83333 
       9 
36.18750

The type argument can also be passed to IQR():
sapply(1:9, \(t) IQR(x, type = t))
[1] 1973.000 1973.000  954.000 1214.500 1714.000 1973.000 1455.000 1800.333
[9] 1778.750

Only 3/9 (types 1, 2, 6) give your result.  (Type 7 is R's default.)
?quantile (and especially Hyndman and Fan 1996, referenced therein) give much more detail about the different definitions.
PS I don't think Normality has anything to do with it ...
While I'm at it, I would be interested if anyone could clarify (in a separate answer or in comments) what "Tukey's recommendations" are in the help for ?IQR: Exploratory Data Analysis is available for checkout at the Internet Archive, but I haven't yet located the precise advice that the R documentation is referring to ...
