Let's go through each part of your question and calculate the requested statistics. Here's the data set representing the radiation emissions (in W/kg) of 11 cell phones:

$0.49, 1.05, 0.22, 1.23, 1.32, 0.38, 1.54, 0.94, 1.11, 0.91, 0.42$

a. Mean

The mean is calculated by summing all the data values and then dividing by the number of values.

$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$ $\text{Mean} = \frac{0.49 + 1.05 + 0.22 + 1.23 + 1.32 + 0.38 + 1.54 + 0.94 + 1.11 + 0.91 + 0.42}{11}$ $\text{Mean} = \frac{9.61}{11} = 0.8736 \, \text{W/kg}$

b. Median

To find the median, we first arrange the data in ascending order:

$0.22, 0.38, 0.42, 0.49, 0.91, 0.94, 1.05, 1.11, 1.23, 1.32, 1.54$

Since there are 11 data points, the median is the value in the middle, which is the 6th value:

$\text{Median} = 0.94 \, \text{W/kg}$

c. Midrange

The midrange is calculated as the average of the lowest and highest values in the data set.

$\text{Midrange} = \frac{\text{Lowest value} + \text{Highest value}}{2}$ $\text{Midrange} = \frac{0.22 + 1.54}{2} = \frac{1.76}{2} = 0.88 \, \text{W/kg}$

d. Mode

The mode is the value that appears most frequently in the data set. In this case, all values are unique, so there is no mode.

e. Discussion about the result in relation to the 1.6 W/kg limit

The computed statistics show the following:

• Mean radiation is 0.8736 W/kg, which is well below the 1.6 W/kg safety limit.
• Median radiation is 0.94 W/kg, indicating that the middle value is also below the safety threshold.
• The Midrange is 0.88 W/kg, also comfortably below 1.6 W/kg.

None of the phones exceed the 1.6 W/kg limit, and the maximum value (1.54 W/kg) is close to the limit but still within safe limits according to current regulations. Thus, it seems that all phones in this sample are considered safe in terms of radiation emissions.

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Would you like more details on any of these calculations or have any specific questions?

Here are 5 related questions you could consider:

1. What is the range of the data (difference between the highest and lowest values)?
2. How would the mean change if an additional phone had radiation of 1.7 W/kg?
3. How does the median compare to the mean in this context?
4. What is the variance or standard deviation of this data set?
5. How could outliers (if any) affect the midrange or mean values?

Tip: The mean can be influenced by extreme values (outliers), whereas the median is more robust in those situations.