A histogram and some computer output provide information about the mercury concentration in the sampled cans (in parts per million, ppm).

(a) Interpret the standard deviation in context.

(b) Determine whether there are any outliers.

(c) Describe the shape, center, and spread of the distribution.

The standard deviation is a statistic that estimates the distribution of information related to its mean and is estimated as the square root of the variance.

a. The standard deviation is given in the output.

$s=0.300$

Interpretation: The mercury concentration in the model cans will generally deviate by $0.300$from the mean mercury concentration.

b.

Given parameters

$$\begin{gathered} Q_1=0.071 \\ {Q}_3=0.380 \end{gathered}$$

The interquartile range is the third quartile decreased by the first quartile:

$IQR=Q_3-Q_1=0.380-0.071=0.309$

Therefore,

$$\begin{gathered} Q_3+1.5IQR=0.380+1.5(0.309)=0.8435 \\ {Q}_1-1.5IQR=0.071-1.5(0.309)=-0.3925 \end{gathered}$$

Since the maximum of 1.500 is higher than 0.8435, it can be known that the maximum is an outlier.

c.

Shape: Right-skewed, because the highest bar in the histogram is to the left and the tail of smaller bars is to the right.

Center: The mean is 0.285 ppm and the median is 0.180 ppm.

Spread: The data take on values between $0.012\mathrm{ppm}$and $1.500\mathrm{ppm}$.