Question

The most obese countries in the world have obesity rates that range from 11.4% to 74.6%. This data is summarized in the following table.

a. What is the best estimate of the average obesity percentage for these countries?

b. The United States has an average obesity rate of 33.9%. Is this rate above average or below?

c. How does the United States compare to other countries?

Short answer

a) The best estimate of the average obesity percentage for these countries is $\overline{X}=23.32.$

b) Since the average for the United Sates is 33.9%, compared to the average obesity rate of 23.32%, the United States has an obesity rate 10.58% greater than average.

c) The obesity rate in the United States is higher than in 84 percent of the countries listed.

Step-by-step solution

Part (a) - Step 1: To find

What is the best estimate of the average obesity percentage for these countries.

Part (a) - Step 2: Explanation

The sample mean is the best estimate of the average in statistics since it is an unbiased approximation of the population mean. In the case of grouped series, the sample mean is calculated using the following formula:

$\overline{x}=\frac{\sum fx}{\sum f}$

To calculate: The sample mean is :

Percent of Population Obese	Number of countries f	Midpoint, x	$fx$
$11.4-20.45$	$29$	$15.925$	$461.83$
$20.45-29.45$	$13$	$24.95$	$324.35$
$29.45-38.45$	$4$	$33.95$	$135.8$
$38.45-47.45$	$0$	$42.95$	$0$
$47.45-56.45$	$2$	$51.95$	$103.9$
$56.45-65.45$	$1$	$60.95$	$60.95$
$65.45-74.45$	$0$	$69.95$	$0$
$74.45-83.45$	$1$	$78.95$	$78.95$
	$\sum f=50$		$\sum fx=1165.78$

$\overline{x}=\frac{1165.78}{50}=23.32$

Therefore the best estimate of the average obesity percentage for these countries is 23.32.

Part (b) - Step 3: To find

Whether the average obesity rate of the United States 33.9 % is above or below the average.

Part(b) - Step 4: Explanation

When we compare the overall average obesity rate to the average obesity rate in the United States, we can clearly see that the average obesity rate in the United States is higher than the global average, at $33.9\%-23.3\%=10.58\%$more than the global average.

Hence the obesity rate in the United States is higher than the global average.

Part (c) - Step 5: To find

How does the United States compare to the other countries

Part (c) - Step 6: Explanation

Looking at the table of data, we can see that there are $29+13=44$ countries out of 50 with obesity rates lower than the United States. As a result, the US has a greater obesity rate than $\frac{44}{50}\times 100=84\%$of the countries listed.