Consider the small set of numbers

\[ 11,14,16,17,18,19,21,24 \]

(a) Compute the 0.25 quantile of this sample using all nine different interpretations of equation (2.11) that are provided in the \(R\) function quantile. (Use the type argument.)

(b) What are the first and third quartiles using the "median of the halves" definition, and what is the IQR by that definition?

(c) Compute the IQR using the quantile R function (with only the default type).
Compute the IQR using the IQR R function.

(d) Compute the IQR and the standard deviation for the daily returns for NFLX for the first calendar quarter 2018.
What is the ratio of the standard deviation to IQR?
How does this compare to the ratio in a normal distribution?

(e) Compute the MAD for the daily returns for NFLX for the first calendar quarter 2018.
What is the ratio of the standard deviation to MAD?
How does this compare to the ratio in a normal distribution?

\(q_\alpha=(1-\gamma) x_{(j: n)}+\gamma x_{((j+1): n)} \tag{2.11}\)