Obesity and Age. A person is said to be overweight if his or...

Obesity and Age. A person is said to be overweight if his or her body mass index (BMI) is between 25 and $29,$ inclusive; a person is said to be obese if his or her BMI is 30 or greater. From the document Utah Behavioral Risk Factor Surveillance System (BRFSS) Local Health District Report, issued by the Utah Department of Health, we obtained the following table. The first two columns of the table provide an age distribution for adults living in Utah. The third column gives the percentage of adults in each age group who are either obese or overweight. $$\begin{array}{|l|c|c|} \hline \text { Age (yr) } & \text { \% adults } & \begin{array}{c} \text { \% obese or } \\ \text { overweight } \end{array} \\ \hline 18-34 & 42.5 & 41.1 \\ 35-49 & 28.5 & 57.9 \\ 50-64 & 16.4 & 68.2 \\ 65 \text { \& over } & 12.6 & 55.3 \\ \hline \end{array}$$ a. What percentage of Utah adults are overweight or obese? b. Of those Utah adults who are between 35 and 49 years old, inclusive, what percentage are overweight or obese? c. Of those Utah adults who are overweight or obese, what percentage are between 35 and 49 years old, inclusive? d. Interpret your answers to parts (a)-(c) in terms of percentages.

Obesity and Age. A person is said to be overweight if his or her body mass index (BMI) is between 25 and $29,$ inclusive; a person is said to be obese if his or her BMI is 30 or greater. From the document Utah Behavioral Risk Factor Surveillance System (BRFSS) Local Health District Report, issued by the Utah Department of Health, we obtained the following table. The first two columns of the table provide an age distribution for adults living in Utah. The third column gives the percentage of adults in each age group who are either obese or overweight.
$$\begin{array}{|l|c|c|}
\hline \text { Age (yr) } & \text { \% adults } & \begin{array}{c}
\text { \% obese or } \\
\text { overweight }
\end{array} \\
\hline 18-34 & 42.5 & 41.1 \\
35-49 & 28.5 & 57.9 \\
50-64 & 16.4 & 68.2 \\
65 \text { \& over } & 12.6 & 55.3 \\
\hline
\end{array}$$
a. What percentage of Utah adults are overweight or obese?
b. Of those Utah adults who are between 35 and 49 years old, inclusive, what percentage are overweight or obese?
c. Of those Utah adults who are overweight or obese, what percentage are between 35 and 49 years old, inclusive?
d. Interpret your answers to parts (a)-(c) in terms of percentages.

Key Concepts

Body Mass Index (BMI)

BMI is a numerical measure that determines whether an individual has a healthy body weight for a given height. It is used as an indicator to classify individuals into categories such as underweight, normal weight, overweight, or obese, which is important for assessing health risks related to body composition.

Weighted Average Calculation

A weighted average calculation involves combining percentages from different subgroups according to the proportions of the overall population that each subgroup represents. This approach is used to compute an overall percentage that accurately reflects the distribution of a characteristic (like being overweight or obese) across various segments of the population.

Population Distribution

Population distribution refers to the breakdown of a total population into subgroups based on characteristics such as age. Knowing the percentage of the total population in each subgroup is critical for understanding how different segments contribute to overall statistics, including health-related metrics.

Conditional Probability

Conditional probability deals with finding the likelihood of an event occurring given that another event has already occurred. In the context of the problem, it may involve computing the percentage of adults in a specific age group who are overweight or obese, or determining what proportion of all overweight or obese individuals belong to that age group.

Interpretation of Percentages

Interpreting percentages means understanding the practical significance of statistical figures. In this context, it involves explaining what the computed percentages indicate about the prevalence of overweight and obesity across different age groups and in the overall population, and how these proportions relate to the broader public health perspective.

Transcript

00:01 All right, in this question, we are given a table of data representing obesity rates in different age groups.

00:07 And when we're given tables like this, we just have to read questions carefully and figure out what information we are trying to pull out.

00:15 So part a asks us what percentage of adults are obese or overweight? so we don't have an overall percentage here, but we do have the percentages segmented by age group.

00:27 And we also have the frequencies of those age groups as a percent.

00:32 So this sets itself up very nicely actually for a weighted average, weighted average, which is simply going to be the values that we're interested in, which is the percentage of obesity.

00:44 So it's the percent obese overweight, weighted by age group.

00:54 What does that mean? well, we're going to take 0 .411.

00:57 That's a 41 .1 is a percentage.

01:00 And we are going to weight it by the prevalence of 18 to 34 of year olds, which is 42 .5%.

01:05 So 0 .425.

01:08 And we're going to add the percentage of obese overweight people, 57 .9%.

01:15 And we are going to weight it by the prevalence of 35 to 49 year olds, so 0 .285.

01:20 We're going to do this for each of our age groups, right? so this is going to be 0 .682, weighted by 16 .4%, so 0 .164.

01:33 And finally, 0 .553 weighted by 12 .6%.

01:40 And when we add all of this together, we will get 0 .521, which is, of course, 52 .1%.

01:48 So this gives us the weighted average over all adults of those who are obese or overweight.

01:55 Now, part b is asking us simply of those of those adults who are between 35 and 49.

02:02 So the important word here are of those between 35 and 49.

02:09 All right.

02:11 We are only interested in those people between the ages of 34 and 49, or 35 and 49, right? so this group right here.

02:28 Now what are we being asked? what percentage are overweight or obese? well, we have that information given right here...

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