Question

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
c.​ midrange
d. mode for the data.
e. Also complete part e

0.75 0.22 1.23 0.64 0.54 0.24 0.81 1.57 0.29 1.02 0.35

e. 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. The minimum data value is the most relevant statistic, because it is closest to the limit of 1 _6Wlkg and that cell phone should be purchased.
2. The maximum data value is the most relevant statistic, because it is closest to the limit of 1 _6W/kg and that cell phone should be avoided.
3. The mean of the data set is the most important statistic because cell phones that have values close to it have the safest emissions.
4. The midpoint of the data set is the most important statistic because cell phones that have values close to it have the safest emissions.

Answer 1

Answer: a. Mean = 0.696364

b. Median = 0.64

c. Midrange = 0.895

d. There is no Mode

e. 2. The maximun data value is the most relevant statistic, because it is closest to the limit of 1.6W/kg and that cell should be avoided.

Explanation:

a) Mean is an average number of the data set, calculated by the sum of all the value divided by the quantity of the set:

mean =
`(0.75+0.22+1.23+0.64+0.54+0.24+0.81+1.57+0.29+1.02+0.35)/(11)`

mean = 0.696364

b) Median is the middle number in the list of numbers. In this case, since there are 11 elements in the set, the middle number is:

sorted numbers of the data set:

0.22 0.24 0.29 0.35 0.54 0.64 0.75 0.81 1.02 1.23 1.57

median = 0.64

c) Midrange is another type of average number. It is calculated as:

midrange =
`(high+low)/(2)`

midrange =
`(1.57+0.22)/(2)`

midrange = 0.895

d) Mode is the number that appears most often in the list of numbers. For this data set, each number appears only one time, so there is no mode.

Mode = 0

e) According to the question, cell phone radiation is dangerous when it is higher than 1.6W/kg. The cell phone with the maximum data value (1.57 W/kg) should be avoided, since it is too close to the limit described.

So, the measures of center are not the most important statistic to be observed but the maximum data value.