each year, forbes magazine compiles a list of the 400 richest americans. as of september 19, 2012, 8 of the…

each year, forbes magazine compiles a list of the 400 richest americans. as of september 19, 2012, 8 of the top 10 on the list are as shown in the accompanying table. determine the range and sample standard deviation. click the icon to view the table of 8 of the top 10 richest americans. the range is $41 billion. (type an integer or a decimal. do not round.) the sample standard deviation is $ billion. (type an integer or a decimal. round to one decimal place as needed.) top 10 richest people in a country person wealth ($ billions) bill gates 66.0 warren buffett 46.0 david koch 31.0 charles koch 31.0 christy walton and family 27.9 alice walton 26.3 s. robson walton 26.1 michael bloomberg 25.0

each year, forbes magazine compiles a list of the 400 richest americans. as of september 19, 2012, 8 of the top 10 on the list are as shown in the accompanying table. determine the range and sample standard deviation. click the icon to view the table of 8 of the top 10 richest americans. the range is $41 billion. (type an integer or a decimal. do not round.) the sample standard deviation is $ billion. (type an integer or a decimal. round to one decimal place as needed.) top 10 richest people in a country person wealth ($ billions) bill gates 66.0 warren buffett 46.0 david koch 31.0 charles koch 31.0 christy walton and family 27.9 alice walton 26.3 s. robson walton 26.1 michael bloomberg 25.0

Answer

Explanation:

Step1: Recall sample - standard deviation formula

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data - points, $\bar{x}$ is the sample mean, and $n$ is the sample size. First, find the sample mean $\bar{x}$. $n = 8$ $\bar{x}=\frac{66.0 + 46.0+31.0 + 31.0+27.9+26.3+26.1+25.0}{8}$ $=\frac{279.3}{8}=34.9125$

Step2: Calculate $(x_{i}-\bar{x})^{2}$ for each $x_{i}$

For $x_1 = 66.0$: $(66.0 - 34.9125)^{2}=(31.0875)^{2}=966.43$ For $x_2 = 46.0$: $(46.0 - 34.9125)^{2}=(11.0875)^{2}=122.93$ For $x_3 = 31.0$: $(31.0 - 34.9125)^{2}=(- 3.9125)^{2}=15.31$ For $x_4 = 31.0$: $(31.0 - 34.9125)^{2}=(-3.9125)^{2}=15.31$ For $x_5 = 27.9$: $(27.9 - 34.9125)^{2}=(-7.0125)^{2}=49.18$ For $x_6 = 26.3$: $(26.3 - 34.9125)^{2}=(-8.6125)^{2}=74.17$ For $x_7 = 26.1$: $(26.1 - 34.9125)^{2}=(-8.8125)^{2}=77.67$ For $x_8 = 25.0$: $(25.0 - 34.9125)^{2}=(-9.9125)^{2}=98.25$

Step3: Calculate $\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}$

$\sum_{i = 1}^{8}(x_{i}-\bar{x})^{2}=966.43+122.93 + 15.31+15.31+49.18+74.17+77.67+98.25$ $=1419.25$

Step4: Calculate the sample standard deviation

$s=\sqrt{\frac{1419.25}{8 - 1}}=\sqrt{\frac{1419.25}{7}}\approx\sqrt{202.75}\approx14.2$

Answer:

14.2