Question

Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L).

1.9 2.3 5.7 5.2 1.9 8.8 3.9 7.3
(a) Find the mean, median, and mode. (Enter your answers to 2 decimal places.)
mean
median
mode
(b) Find the sample standard deviation, coefficient of variation, and range. (Enter your answers to 2 decimal places.)
s
CV %
range

Answer 1

a)
`\bar{x}`=4.63 md=4.55 mo= 1.9 b) Sample Standard Deviation≈ 2.58 Coefficient of Variation=55.72% Sample Range=6.9

Explanation:

a)

Mean

`a)\bar{x}=(1.9+ 2.3+ 5.7+ 5.2+ 1.9+ 8.8+ 3.9+ 7.3)/(8) =(37)/(8)=4.625=\approx 4.63`

For the Median, we have to order the entries. So, ordering it goes:

1.9 1.9 2.3 3.9 5.2 5.7 7.3 8.8

Since we have even entries
`((n)/(2)+(n)/(2) +1)/(2)=(4th+5th)/(2)=(3.9+5.2)/(2)=4.55`

mode

The mode for this data 1.9 1.9 2.3 3.9 5.2 5.7 7.3 8.8 is 1.9

b)

Sample Standard Deviation

Here it is the formula to calculate it:

`_(x)=\sqrt{\frac{\sum (x_(i)-\bar{x})^(2)}{n-1}}\\ S_(x)=\sqrt{(46.855)/(7)}\approx 2.58`

Coefficient of Variation

CV is the quocient between sample Standard deviation over Mean and it is used to make comparisons.

`CV=\frac{S_x}{\bar{x}}*100%=(2.58)/(4.63) \approx 55.72%`

Range

The difference between the highest and the lowest value of this sample

8.8-1.9=6.9