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? 0.83 1.39 1.39 1.03 0.66 1.26 1.39 1.18 1.41 1.19 1.15

Answer 1

`Range =1.41-0.66 = 0.75`

`\bar X = 1.171 W/Kg`

`s^2 = 0.0607`

And taking the square root we got the sample deviation:

`s = √(0.0607)= 0.246 W/kg`

Explanation:

For this case we have the following datset given:

0.83 1.39 1.39 1.03 0.66 1.26 1.39 1.18 1.41 1.19 1.15

We need to find the range, and the range is defined by:

`Range = Max -Min`

And replacinng we got:

`Range =1.41-0.66 = 0.75`

Then we can find the sample variance, but firt we need to find the sample mean with this formula:

`\bar X = (\sum_(i=1)^n X_i)/(n)`

And replacing we got:

`\bar X = 1.171 W/Kg`

Now we can find the sample variance with this formula:

`s^2 = (\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)`

And replacing we got:

`s^2 = 0.0607`

And taking the square root we got the sample deviation:

`s = √(0.0607)= 0.246 W/kg`