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Expert-verified Found in: Page 153 ### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208 # The most obese countries in the world have obesity rates that range from 11.4% to 74.6%. This data is summarized in Table 14. What is the best estimate of the average obesity percentage for these countries? What is the standard deviation for the listed obesity rates? The United States has an average obesity rate of 33.9%. Is this rate above average or below? How “unusual” is the United States’ obesity rate compared to the average rate? Explain.

Estimate of average obesity percentage is $=23.3155.$

Sample standard deviation $=12.8238$

The Unites States average obesity rate is above average obesity rate.

See the step by step solution

## Step 1: To determine

Obesity rate standard deviation and average obesity percentage are best estimates. Also, to determine the difference between the obesity rate in the United States and the global obesity rate.

## Step 2: Explanation

The given percentage obesity rate class and number of countries under each class. Calculation:

The estimate of average obesity percentage for countries is sample mean. The formula to find sample mean from frequency table is

Sample mean $\overline{x}=\frac{\sum f{x}_{m}}{n}$

Where

$\mathrm{f}=$ class frequency,

${x}_{m}=$ class midpoint and

$\mathrm{n}=$ total frequency

The formula to find standard deviation for grouped frequency data is

Standard deviation role="math" localid="1648086234307" $\mathrm{s}=\sqrt{\frac{\sum {{f}_{{x}_{m}}}^{2}}{n}-{\overline{x}}^{2}}$

## Step 3: To find sample mean and standard deviation

consider the table: Calculate the sample mean:

$\begin{array}{r}\overline{x}=\frac{\sum f{x}_{m}}{n}\\ =\frac{1165.775}{50}\\ =23.3155\end{array}$

So, sample mean = $23.3155$

To calculate standard deviation the formula is shown below:

$s=\sqrt{\frac{\sum f{x}^{2}}{n}-{\overline{x}}^{2}}$

Substitute values as shown below:

role="math" localid="1648086750018" $s=\sqrt{\frac{\sum f{x}^{2}}{n}-{\overline{x}}^{2}}\phantom{\rule{0ex}{0ex}}\begin{array}{r}=\sqrt{\frac{35403.1}{50}-\left(23.32{\right)}^{2}}\\ =\sqrt{708.062-543.8224}\\ =12.82\end{array}$

Hence the value standard deviation = 12.82

The average obesity rate in the United States is 33.9 percent. For the given countries, the average rate is 23.3155. The average obesity rate in the United States is higher than other countries.

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