Questions: 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 W/kg or less. Find the a. mean, b. median, and c. mode for the data. Also complete part d. 0.21, 1.24, 0.92, 0.75, 0.52, 0.55, 1.48, 1.45, 1.22, 0.83, 1.56 d. If you are planning to purchase a cell phone, are any of the measures of center the most important statistic? Is there another statistic that is most relevant? If so, which one? A. The minimum data value is the most relevant statistic, because it is closest to the limit of 1.6 W/kg and that cell phone should be purchased. B. The mean of the data set is the most important statistic because cell phones that have values close to it have the safest emissions.

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 W/kg or less. Find the a. mean, b. median, and c. mode for the data. Also complete part d. 0.21, 1.24, 0.92, 0.75, 0.52, 0.55, 1.48, 1.45, 1.22, 0.83, 1.56 d. If you are planning to purchase a cell phone, are any of the measures of center the most important statistic? Is there another statistic that is most relevant? If so, which one? A. The minimum data value is the most relevant statistic, because it is closest to the limit of 1.6 W/kg and that cell phone should be purchased. B. The mean of the data set is the most important statistic because cell phones that have values close to it have the safest emissions.
Transcript text: 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 W/kg or less. Find the a. mean, b. median, and c. mode for the data. Also complete part $d$. $\begin{array}{lllllllllll}0.21 & 1.24 & 0.92 & 0.75 & 0.52 & 0.55 & 1.48 & 1.45 & 1.22 & 0.83 & 1.56\end{array}$ d. If you are planning to purchase a cell phone, are any of the measures of center the most important statistic? Is there another statistic that is most relevant? If so, which one? A. The minimum data value is the most relevant statistic, because it is closest to the limit of $1.6 \mathrm{~W} / \mathrm{kg}$ and that cell phone should be purchased. B. The mean of the data set is the most important statistic because cell phones that have values close to it have the safest emissions.
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Solution

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Solution Steps

Step 1: Calculate the Mean

The mean \( \mu \) of the radiation emissions is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of observations and \( x_i \) are the individual data points. For the given data:

\[ \mu = \frac{10.73}{11} = 0.98 \]

Step 2: Calculate the Median

To find the median, we first sort the data:

\[ \text{Sorted data} = [0.21, 0.52, 0.55, 0.75, 0.83, 0.92, 1.22, 1.24, 1.45, 1.48, 1.56] \]

The median is the value at the position given by the formula:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (11 + 1) = 6.0 \]

The quantile is at position 6, which corresponds to the value:

\[ \text{Median} = 0.92 \]

Step 3: Calculate the Mode

The mode is the value that appears most frequently in the dataset. In this case, the mode is:

\[ \text{Mode} = 0.21 \]

Final Answer

The calculated statistics are:

  • Mean: \( \mu = 0.98 \)
  • Median: \( 0.92 \)
  • Mode: \( 0.21 \)

Thus, the final answer is:

\[ \boxed{\text{Mean} = 0.98, \text{Median} = 0.92, \text{Mode} = 0.21} \]

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