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An experimental study of the atomization characteristics of biodiesel fuel was aimed at reducing the pollution produced by diesel engines. Biodiesel fuel is recyclable and has low emission characteristics. One aspect of the study is the droplet size $(\mu \mathrm{m})$ injected into the engine, at a fixed distance from the nozzle. From data provided by the authors on droplet size, we consider a sample of size 41 that has already been ordered.

$\begin{array}{lllllllll}2.1 & 2.2 & 2.2 & 2.3 & 2.3 & 2.4 & 2.5 & 2.5 & 2.5 \\ 2.8 & 2.9 & 2.9 & 2.9 & 3.0 & 3.1 & 3.1 & 3.2 & 3.3 \\ 3.3 & 3.3 & 3.4 & 3.5 & 3.6 & 3.6 & 3.6 & 3.7 & 3.7 \\ 4.0 & 4.2 & 4.5 & 4.9 & 5.1 & 5.2 & 5.3 & 5.7 & 6.0 \\ 6.1 & 7.1 & 7.8 & 7.9 & 8.9 & & & & \end{array}$

(a) Group these droplet sizes and obtain a frequency table using $[2,3),[3,4),[4,5)$ as the first three classes, but try larger classes for the other cases. Here the left-hand endpoint is included but the right-hand endpoint is not.
(b) Construct a density histogram.
(c) Obtain $\bar{x}$ and $s^{2}$.
(d) Obtain the quartiles.
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