Question

2.10 \( \bar{x}\) and \(\mathrm{s}\) by Hand. Radon is a naturally occurring gas and is the second leading cause of lung cancer in the United States. I It comes from the natural breakdown of uranium in the soil and enters buildings through cracks and other holes in the foundations. Found throughout the United States, levels vary considerably from state to state. Several methods can reduce the levels of radon in your home, and the Environmental Protection Agency recommends using one of these if the measured level in your home is above 4 picocuries per liter. Four readings from Franklin County, Ohio, where the county average is \(8.4\) picocuries per liter, were \(7.1,11.6,8.1\), and \(13.4\).

(a) Find the mean step-by-step. That is, find the sum of the four observations and divide by 4 .

(b) Find the standard deviation step-by-step. That is, find the deviation of each observation from the mean, square the deviations, then obtain the variance and the standard deviation. Example 2.7(page 58 ) shows the method.

(c) Now enter the data into your calculator and use the mean and standard deviation buttons to obtain \(\bar{x}\) and \(s\). Do the results agree with your hand calculations?

Answer 1

I calculated all calculations by hand and cross validited with Excel

I enter all data in to Excel and

use syntax =AVERAGE (number1,number2.....) for mean and

=stdev.p(number1,number2.....) for standard daviation