Question

Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results.Listed below are the measured radiation absorption rates​ (in W/kg) corresponding to various cell phone models. If one of each model is measured for radiation and the results are used to find the measures of​ variation, are the results typical of the population of cell phones that are in​ use?0.950.950.730.730.630.630.910.911.321.321.481.480.630.631.231.230.910.911.411.410.670.67The range of the sample data isnothing▼​(Round to three decimal places as​ needed.)Sample standarddeviationequals=nothing▼kg.kg.left parenthesis Upper W divided by kg right parenthesis squared .W/kg2.W.W.Upper W divided by kg.W/kg.​(Round to three decimal places as​ needed.)Samplevarianceequals=nothing▼kg.kg.left parenthesis Upper W divided by kg right parenthesis squared .W/kg2.Upper W divided by kg.W/kg.W.W.​(Round to three decimal places as​ needed.)If one of each model is measured for radiation and the results are used to find the measures of​ variation, are the results typical of the population of cell phones that are in​ use?A.​No, because it is necessary to have at least 5 of each cell phone in order to get a meaningful result. Only including one of each cell phone model is not representative of each cell phone model.B.​Yes, because the results from any sample of cell phones will be typical of the population.C.​Yes, because each model is being represented in the sample. Any sample that considers all possible cell phone models will produce results typical of the population of cell phones.D.​No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.

Answer 1

D.​No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.

Explanation:

(a) Range is the difference between the smallest and largest observation.

Here Smallest observation = 0.63

and Largest observation = 1.48

⇒ Range = 0.85

(b) Standard Deviation is calculate by,

`Standard deviation(\sigma) = \sqrt{(1)/(n)\sum_(i=1)^(n){(x_(i)-\bar{x})^(2)} }`

where,
`\bar{x}` is mean of the observation.

Here, Mean = 0.988

⇒ Standard Deviation = 0.313

(c) Variance is the square of Standard deviation.

Thus, Variance = (Standard Deviation)² = 0.098

(d) Here last option(D) is true i.e. ​No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.