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Twenty brands of soft drinks resulted in the following caffeine amounts:

(a)

Mean is computed using the formula given below.

$\stackrel{炉}{x}=\frac{鈭�x}{n}$, where xrepresents the observations and nis the count of the observations.

Substitute the values in the formula.

$$\begin{gathered} \stackrel{炉}{x}=\frac{0+0+...+47}{20} \\ =\frac{651}{20} \\ =32.55 \\ 鈮�32.6 \end{gathered}$$

Thus, the mean value is approximately 32.6 mg.

(b)

Median is computed using the following criteria:

• Median is equal to the middlemost observation when n is an odd value.
• Median is equal to the average of the two middle observations when n is an even value.

The number of observations is 20.

Arrange the observations in ascending order.

The middlemost observations are 38 and 41.

The median is given as:

$$\begin{gathered} M=\frac{38+41}{2} \\ =\frac{79}{2} \\ =39.5 \end{gathered}$$

Thus, the median is 39.5 mg.

(c)

The observation with the maximum frequency is the mode.

The frequency distributionsfor the amount of caffeine are:

The highest frequency is obtained for 0mg.

Thus, the mode of the data is 0 mg.

(d)

The midrange is computed using the following formula:

$\text{Midrange}=\frac{\text{Minimum}\text{value}+\text{Maximum}\text{value}}{2}$

Substitute the values in the formula.

$$\begin{gathered} \text{Midrange}=\frac{0+55}{2} \\ =27.5 \end{gathered}$$

Thus, the midrange is 27.5 mg.

The statistics are not representative of the population because of the following:

• The brands evaluated in the study are not stated, and there are high chances that few brands are much more popular than the others.
• The quantity of caffeine in each of the cans from various brands may differ.

Inferring from the above points, the statistics are not a true representative of the population.