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?

49
40
34
30
0
34
33
59
56
39
46
53
0
0

The range of the sample data is

nothing

▼

brands squared .brands2.

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

left parenthesis mg per 12 oz of drink right parenthesis squared .(mg per 12oz of drink)2.

brands.brands.

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

The standard deviation of the sample data is

nothing

▼

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

left parenthesis mg per 12 oz of drink right parenthesis squared .(mg per 12oz of drink)2.

brands squared .brands2.

brands.brands.

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

The variance of the sample data is

nothing

▼

brands.brands.

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

left parenthesis mg per 12 oz of drink right parenthesis squared .(mg per 12oz of drink)2.

brands squared .brands2.

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

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

A.

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.

B.

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.

C.

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.

D.

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.

Click to select your answer(s).

Answer 1

Solution: Given that 49,40,34,30,0,34,33,59,56,39,46,53,0,0

=> The range of the sample data is 59

Explanation

The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

0 0 0 30 33 34 34 39 40 46 49 53 56 59   

The lowest value is 0.

The highest value is 59.

The range = 59 - 0 = 59.

=> The standard deviation of the sample data is 20.4

=> The variance of the sample data is 414.2

=> option B. 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