## Related questions with answers

Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, ... , Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans?

$\begin{matrix} \text{0} & \text{0} & \text{34} & \text{34} & \text{34} & \text{45} & \text{41} & \text{51} & \text{55} & \text{36} & \text{47} & \text{41} & \text{0} & \text{0} & \text{53} & \text{54} & \text{38} & \text{0} & \text{41} & \text{47}\\ \end{matrix}$

Solution

VerifiedThe range is the difference between the highest and lowest data value:

$RANGE=55-0=55$

The mean is the sum of all values divided by the number of values:

$\overline{x}=\dfrac{0+0+34+34+34+45+...+38+0+41+47}{20}=\dfrac{651}{20}\approx 32.55$

$n$ is the number of values in the data set.

$n=20$

The variance is the sum of squared deviations from the mean divided by $n-1$:

$s^2=\dfrac{(0-32.55)^2+....+(47-32.55)^2}{20-1}\approx 413.4184$

The standard deviation is the square root of the variance:

$s=\sqrt{s^2}=\sqrt{413.4184}\approx 20.3327$

The statistics are not representative for the population of all cans consumed, because some brands will be preferred over others by Americans.

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