In Exercises, find the range, variance, and standard deviation for the given samph data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-2 where we found measures of center. Here we find measures of variation.) Then answer the given questions.

Cell Phone Radiation Listed below are the measured radiation emissions (in W/kg) corresponding to these cell phones: Samsung SGH-tss9, Blackberry Storm, Blackberry Curve, Motorola Moto, T-Mobile Sidekick, Sanyo Katana Eclipse, Palm Pre, Sony Ericsson, Nokia 6085, Apple iPhone 3G S, and Kyocera Neo El 100. The data are from the Environmental Working Group. If one of each model of cell phone is measured for radiation and the results are used to find the standard deviation, is that standard deviation equal to the standard deviation of the population of all cell phones that are in use? Why or why not?

Answer :

Step 1 of 1 :

Given Cell Phone Radiation Listed below are the measured radiation emissions (in W/kg) corresponding to these cell phones: Samsung SGH-tss 9, Blackberry Storm, Blackberry Curve, Motorola Moto, T-Mobile Sidekick, Sanyo Katana Eclipse, Palm Pre, Sony Ericsson, Nokia 6085, Apple iPhone 3G S, and Kyocera Neo El 100.

The data are from the Environmental Working Group.

0.38 , 0.55 , 1.54 , 0.50 , 0.60 , 0.92 , 0.96 , 1.00 , 0.86 , 1.46

Now we have to find the range, variance, and standard deviation for the given sample data.

The range is a simple measure of variation in a set of random variables. It is difference between the biggest and smallest random variable.

Range = Maximum value - Minimum value

Given data

0.38 , 0.55 , 1.54 , 1.55 , 0.50 , 0.60 , 0.92 , 0.96 , 1.00 , 0.86 , 1.46

Range = Maximum value - Minimum value

Range = 1.55 - 0.38

Range = 1.17

Therefore range is 1.17.

Sample variance :

The variance of a sample is defined by slightly different formula:

The sample variance is the square difference of the data value to the mean divided by the number of values.

s2 =

where s2 is the sample variance.

x is the sample mean.

xi is the ith element from the sample and

n is the number of elements in the sample.

0.38 + 0.55 + 1.54 + 1.55 + 0.50 + 0.60 , 0.92 + 0.96 + 1.00 + 0.86 + 1.46

Sum = 10.32

=

=