Question

Listed below are measured amounts of caffeine​ (mg per 12oz of​ drink) obtained in one can from each of 14 brands. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are the statistics representative of the population of all cans of the same 14 brands​ consumed?

5656

3939

4343

5555

00

6060

4646

5050

3535

5656

3838

5555

00

00

-The range of the sample data is

6060 mg per 12 oz of drink.mg per 12oz of drink.

​(Round to one decimal place as​ needed.)

-The standard deviation of the sample data is?

​(Round to one decimal place as​ needed.)

-The variance of the sample data is?

Are the statistics representative of the population of all cans of the same 14 brands​ consumed?

A.The statistics are not necessarily representative of the population of all cans of these brands that are consumed because each brand is weighted equally in the calculations. It is unlikely that each of the 14 brands of soda are consumed equally.

B.The statistics are likely representative of the population of all cans of these brands that are consumed because each brand is being represented in the sample.

C.The statistics are likely representative of the population of all cans of these brands that are consumed because the results from any sample of the 14 brands will be typical of the population.

D.The statistics are not necessarily representative of the population of all cans of these brands that are consumed because it is necessary to have at least 5 of each brand in order to get a sample that is representative of the population.

Answer 1

The statistical software output for this problem is:

Summary statistics:

Column	Range	Variance	Std. dev.
Data	60	305.33333	17.47379

Hence,

Range = 60

Standard deviation = 17.5

Variance = 305.3

The statistics are not necessarily representative of the population of all cans of these brands that are consumed because each brand is weighted equally in the calculations. It is unlikely that each of the 14 brands of soda are consumed equally. Option A is correct.