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<aside> 📝 Here you see four boxplots, each based on datasets of size 200. There is a question on each of them.
a) Is this statement true? In boxplot I we have that $m\ge p_{0.25}-1.5*IQR$. Here $m$ is the minimum, $p_{0.25}$ the 25-percentile and $IQR$ the interquartile range.
b) Is this statement true? In boxplot II the median is smaller than the mean.
c) Here you can use that boxplot III is taken from a $N(\mu,\sigma^2)$ distribution.
The IQR in this boxplot is 8. Based on this, a good estimate for $\sigma$ is approximately:
$4\quad 8\quad 3\quad 5\quad 7\quad 6$
d) Boxplot IV is based on the dataset $x_1,x_2,\ldots,x_{200}$.
Statement: if we draw the boxplot of the absolute values of these observations, $|x_1|,|x_2|,\ldots,|x_{200}|$, then the median will stay at the same value.
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Approximate $\sigma$ and $\mu$.
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