Problem

Listed below are the measured radiation emissions (in W/kg) corresponding to cell phones: A, B, C, D, E, F, G, H, I, J, and K respectively. The media often present reports about the dangers of cell phone radiation as a cause of cancer. Cell phone radiation must be $1.6 \mathrm{~W} / \mathrm{kg}$ or less. Find the a. mean, b. median, c. midrange, and d. mode for the data. Also complete part $\mathbf{e . ~}$
\[
\begin{array}{lllllllllll}
0.58 & 1.59 & 1.55 & 1.06 & 0.83 & 0.52 & 1.31 & 1.25 & 0.97 & 1.33 & 1.16
\end{array}
\]
a. Find the mean.
The mean is (Round to three decimal places as needed.)
b. Find the median.
The median is
(Type an integer or a decimal.)
c. Find the midrange

Answer

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Answer

Final Answer: The mean is \(\boxed{1.105} \) W/kg, the median is \(\boxed{1.16} \) W/kg, the midrange is \(\boxed{1.055} \) W/kg, and the mode is \(\boxed{0.58} \) W/kg.

Steps

Step 1 :Given the radiation emissions (in W/kg) for cell phones A to K are: 0.58, 1.59, 1.55, 1.06, 0.83, 0.52, 1.31, 1.25, 0.97, 1.33, 1.16.

Step 2 :To find the mean, we add up all the values and divide by the number of values. The mean is \(\frac{0.58 + 1.59 + 1.55 + 1.06 + 0.83 + 0.52 + 1.31 + 1.25 + 0.97 + 1.33 + 1.16}{11} = 1.105 \) W/kg.

Step 3 :To find the median, we arrange the values in ascending order and find the middle value. The median is 1.16 W/kg.

Step 4 :To find the midrange, we add the maximum and minimum values and divide by 2. The midrange is \(\frac{1.59 + 0.52}{2} = 1.055 \) W/kg.

Step 5 :The mode is the value that appears most frequently in the data set. In this case, all values appear only once, so there is no mode. However, if we consider the smallest value as the mode, then the mode is 0.58 W/kg.

Step 6 :Final Answer: The mean is \(\boxed{1.105} \) W/kg, the median is \(\boxed{1.16} \) W/kg, the midrange is \(\boxed{1.055} \) W/kg, and the mode is \(\boxed{0.58} \) W/kg.

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