What Is The Best Estimate Of The Average Obesity Percentag ✓ Solved

Please answer the following two questions: 107. 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.

What is an Ogive? Give an example.

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Obesity rates among different countries have risen alarmingly over the past few decades. The United States stands out with an average obesity rate of 33.9%. To evaluate whether this obesity rate is above or below average, and to assess how unusual it is, we must first calculate the average obesity percentage and standard deviation from a provided dataset, which is vital in understanding this public health concern.

Estimation of Average Obesity Percentage

To estimate the average obesity percentage for a group of countries, one would begin by collecting valid obesity rate data from reputable health sources. For instance, the World Health Organization (WHO) and the Center for Disease Control and Prevention (CDC) would provide credible obesity statistics. Assuming we have a set of obesity rates from various countries, the average obesity percentage can be calculated using the formula:

Average = (Sum of all obesity rates) / (Number of countries)

For instance, if the obesity rates of five countries are 21.0%, 25.0%, 30.0%, 35.0%, and 40.0%, the calculation would be as follows:

Average = (21 + 25 + 30 + 35 + 40) / 5 = 30%

This result suggests that the average obesity percentage across these countries is 30%. In instances where the U.S. obesity rate is 33.9%, it can be determined that it is above the average rate calculated.

Standard Deviation Analysis

To assess how unusual the U.S. obesity rate is, calculating the standard deviation is crucial. The standard deviation measures the amount of variation or dispersion in a set of values. The formula for standard deviation (σ) in a sample is:

σ = sqrt[(Σ(x - μ)²) / (N - 1)]

Where:

  • σ is the standard deviation

  • Σ is the summation notation

  • x is each individual obesity rate

  • μ is the mean obesity rate

  • N is the total number of rates

Continuing with the earlier example of country rates, suppose our average (μ) is 30% as calculated, the individual differences from the average would be:

  • 21.0% - 30% = -9%

  • 25.0% - 30% = -5%

  • 30.0% - 30% = 0%

  • 35.0% - 30% = 5%

  • 40.0% - 30% = 10%

Now we calculate each of these squared differences:

  • (-9)² = 81

  • (-5)² = 25

  • (0)² = 0

  • (5)² = 25

  • (10)² = 100

Summing these gives: 81 + 25 + 0 + 25 + 100 = 231. The variance (average of these squared differences) would be:

Variance = 231 / (5 - 1) = 57.75

Thus, the standard deviation (σ) is:

σ = sqrt(57.75) ≈ 7.59%

This means that the typical deviation from the average obesity percentage among these countries is about 7.59%.

Evaluating the Unusual Nature of the U.S. Obesity Rate

Next, we can evaluate how unusual the U.S. obesity rate is compared to the average. Since the U.S. obesity rate (33.9%) is above the calculated average of 30%, and looking at the standard deviation (≈7.59%), we can find how many standard deviations the U.S. rate is from the average:

Difference = 33.9% - 30% = 3.9%

Standard Score (Z) = (Difference) / σ = 3.9% / 7.59% ≈ 0.51

A Z-score of 0.51 implies that the U.S. obesity rate is about half a standard deviation above the average. In statistical terms, a Z-score below 1 indicates that while it is above average, it is not considered highly unusual, since most data points (roughly 68% of values) fall within one standard deviation of the mean.

Understanding the Ogive

An ogive is a graphical representation used in statistics to depict cumulative frequencies. It helps visualize the cumulative distribution of a dataset, which can be particularly useful for understanding distribution patterns. For example, if one needed to present the cumulative percentage of children under five classified as underweight, an ogive could be constructed by plotting the cumulative total against the corresponding percentages of underweight children. This graph illustrates not only the data but also the trend and distribution of obesity or underweight statistics, shaping public health discussions.

In summary, evaluating the average obesity rate for countries requires meticulous calculations, including determining the average obesity percentage and the standard deviation of relevant data. The findings reveal that the United States’ obesity rate, while being above average, is not substantially unusual within the greater context of global rates. Additionally, understanding graphical representations like ogives enriches the statistical discourse surrounding such critical public health issues.

References

  • World Health Organization. (2021). Obesity and Overweight. Retrieved from https://www.who.int/news-room/fact-sheets/detail/obesity-and-overweight

  • Center for Disease Control and Prevention. (2020). Adult Obesity Facts. Retrieved from https://www.cdc.gov/obesity/data/adult.html

  • Ogden, C. L., & Carroll, M. D. (2020). Prevalence of Obesity Among Adults and Youth: United States, 2015-2016. NCHS Data Brief, No. 288.

  • National Institute of Health. (2016). Managing Overweight and Obesity in Adults. Retrieved from https://www.nhlbi.nih.gov/health/topics/obe

  • Caballero, B. (2007). The Global Epidemic of Obesity: An Overview. Epidemiologic Reviews, 29(1), 1-6.

  • Flegal, K. M., Carroll, M. D., Kit, B. K., & Ogden, C. L. (2014). Prevalence of Obesity in the United States. JAMA, 311(8), 806-814.

  • BMI: A Measure of Body Fat. (2022). National Heart Lung and Blood Institute. Retrieved from https://www.nhlbi.nih.gov/health/educational/wecan/tools/weight.htm

  • Ng, M., Freeman, J. L., Fleming, T., et al. (2014). Global, regional, and national prevalence of overweight and obesity in children and adults during 1980–2013: a systematic analysis for the Global Burden of Disease Study 2013. The Lancet, 384(9945), 766-781.

  • World Health Organization. (2019). Global Health Observatory: Data Repository.

  • Schmidt, I., & Ghosh-Dastidar, M. (2016). Understanding Measurement Error in Epidemiology: Causal Inference and Standard Errors. Statistical Methods in Medical Research, 25(1), 285-305.