Answer to Question #143879 in Statistics and Probability for Vladimyr Lubin

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?
0.74,0.72,1.38,0.67,1.09,0.76,1.08,0.96,0.74,0.98,0.87

Answer 1

The range is the difference between the highest and the lowest value(see https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/range-statistics/). In our case it is: $r=1.38-0.67=0.71$.

The mean is(see https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php):

$\bar{x}=\frac{0.74+0.72+1.38+0.67+1.09+0.76+1.08+0.96+0.74+0.98+0.87}{11}\approx0.9082\,\,W/kg.$

The variance is (https://www.sciencebuddies.org/science-fair-projects/science-fair/variance-and-standard-deviation):

$\sigma^2=((0.74-0.9082)^2+(0.72-0.9082)^2+(1.38-0.9082)^2+(0.67-0.9082)^2+(1.09-0.9082)^2+(0.76-0.9082)^2+(1.08-0.9082)^2+(0.96-0.9082)^2+(0.74-0.9082)^2+(0.98-0.9082)^2+(0.87-0.9082)^2)/11\approx0.0423\,\,(W/kg)^2.$

The standard deviation is the square root of variance:

$\sigma\approx0.2056\,\,W/kg$.

In order to make any assumptions regarding the population of the cel phones, it is better to use bigger sample data. It is also important to know, whether any criterions were used, while making the data: e.g., whether all samples belong to the same company, etc.

Answer: 0.71; 0.0423; 0.2056