Question

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

Cell Phone Radiation Listed below are the measured radiation absorption rates (in W>kg) corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the Federal Communications Commission (FCC). The media often report about the dangers of cell phone radiation as a cause of cancer. The FCC has a standard that a cell phone absorption rate must be 1.6 W>kg or less. 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?

1.18 1.41 1.49 1.04 1.45 0.74 0.89 1.42 1.45 0.51 1.38

Short answer

(a) The mean is 1.178 W/kg.

(b) The median is 1.380 W/kg.

(c) The mode is 1.45 W/kg.

(d) The midrange is 1.000 W/kg.

Mean is the center measure that is the most important to evaluate.

The other relevant measure is the lowest value of the radiation

Step-by-step solution

Given information

The cell phones which FCC measured for absorption rate in W/kg are:

iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme.

The measured radiation absorption rates for the 11 cell phones:

1.18, 1.41, 1.49, 1.04, 1.45, 0.74, 0.89, 1.42, 1.45, 0.51, 1.38

Also, the standard absorption rate is 1.6 W/kg or lower.

Compute mean

(a)

The mean for a set of sampled observations is computed as:

$\overline{x}=\frac{\sum x}{n}$, where x represents the observations and n is the count of the observations.

Substitute the values in the formula.

$$\begin{gathered} \overline{x}=\frac{1.18+1.41+...+1.38}{11} \\ =\frac{12.96}{11} \\ \approx 1.178 \end{gathered}$$

Thus, the mean value is approximately 1.178 W/kg.

Compute median

(b)

The median for a set of observations arranged in ascending (or descending) order is computed as:

• The middlemost observation is the median if n is known to be odd.
• The average of two middle observations is the median if n is known to be even.

The number of observations is11.

Arrange the observations in ascending order.

0.51
0.74
0.89
1.04
1.18
1.38
1.41
1.42
1.45
1.45
1.49

The middlemost observation is 1.38.

The median is given as:

$M=1.38$

Thus, the median is 1.380 W/kg.

Compute mode

(c)

The observation that repeats the most is the mode.

The frequency distributions of the data are given as:

Radiation absorption rates	Frequency
0.51	1
0.74	1
0.89	1
1.04	1
1.18	1
1.38	1
1.41	1
1.42	1
1.45	2
1.49	1

The highest frequency is obtained as1.45.

Thus, the mode of the data is 1.45W/kg.

Compute midrange

(d)

The midrange for a set of observations is computed as:

$\text{Midrange}=\frac{\text{Minimum}\text{value}+\text{Maximum}\text{value}}{2}$

Substitute the values in the formula.

$$\begin{gathered} \text{Midrange}=\frac{0.51+1.49}{2} \\ =\frac{2}{2} \\ =1 \end{gathered}$$

Thus, the midrange is 1.000 W/kg.

Explain which of the measures for the center are the most important

The mean of the radiation absorption rates is one of the most important measures to consider while purchasing a cell phone.

The mean would suggest an idea of how large the absorption rate is for any particular cell phone. While purchasing any specific phone, the absorption rate can be compared to the mean value.

State another statistic most relevant in this case

Another most relevant statistic is the lowest radiation absorption rate of the phone. It would help the buyer judge the lowest rate among the different cell phone brands in the market.