Solved on Nov 15, 2023

(a) The most obese countries have obesity rates ranging from $11.4\%$ to $74.6\%$ . Estimate the average obesity percentage. (Round to 2 decimal places)
(b) The US obesity rate is $33.9\%$ . Is this above or below average? above average below average
(c) The US has an obesity rate higher than at least $\%$ of the countries in the data set.

STEP 1

Assumptions1. The table provides the range of obesity rates and the number of countries in each range. . The best estimate of the average obesity percentage for these countries can be calculated by taking the midpoint of each range, multiplying it by the number of countries in that range, and then dividing the sum of these products by the total number of countries.
3. The obesity rate of the United States is $33.9\%$ .

STEP 2

First, we need to find the midpoint of each range. The midpoint is the average of the lower and upper bounds of the range.
$Midpoint = \frac{{Lower\, bound + Upper\, bound}}{2}$

STEP 3

Calculate the midpoints for each range.
For the first range $11.-20.45$ , the midpoint is $Midpoint = \frac{{11. +20.45}}{2}$ Repeat this calculation for all other ranges.

STEP 4

Next, multiply each midpoint by the number of countries in that range.
$Product = Midpoint \times Number\, of\, countries$

STEP 5

Calculate the products for each range.
For the first range, the product is $Product = Midpoint \times28$ Repeat this calculation for all other ranges.

STEP 6

Add up all the products to get the total sum.
$Total\, sum = \sum Product$

STEP 7

Calculate the total number of countries by adding up the number of countries in each range.
$Total\, number\, of\, countries = \sum Number\, of\, countries$

STEP 8

Now, divide the total sum by the total number of countries to get the best estimate of the average obesity percentage.
$Average\, obesity\, percentage = \frac{{Total\, sum}}{{Total\, number\, of\, countries}}$

STEP 9

Round the average obesity percentage to two decimal places.

STEP 10

To determine whether the obesity rate of the United States is above or below average, compare the obesity rate of the United States ( $33.9\%$ ) with the average obesity percentage.

STEP 11

To determine how the United States compares to other countries, find the range in which the obesity rate of the United States falls. Then, add up the number of countries in all ranges below that range and the number of countries in that range itself. Divide this sum by the total number of countries and multiply by100 to get the percentage.
$Percentage = \frac{{\sum Number\, of\, countries\, in\, ranges\, below\, and\, in\, the\, range\, of\, the\, United\, States}}{{Total\, number\, of\, countries}} \times100$

STEP 12

Round the percentage to the nearest whole number.

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STEP 1

STEP 2

First, we need to find the midpoint of each range. The midpoint is the average of the lower and upper bounds of the range.
$Midpoint = \frac{{Lower\, bound + Upper\, bound}}{2}$

STEP 3

Calculate the midpoints for each range.
For the first range $11.-20.45$ , the midpoint is $Midpoint = \frac{{11. +20.45}}{2}$ Repeat this calculation for all other ranges.

STEP 4

Next, multiply each midpoint by the number of countries in that range.
$Product = Midpoint \times Number\, of\, countries$

STEP 5

Calculate the products for each range.
For the first range, the product is $Product = Midpoint \times28$ Repeat this calculation for all other ranges.

STEP 6

Add up all the products to get the total sum.
$Total\, sum = \sum Product$

STEP 7

Calculate the total number of countries by adding up the number of countries in each range.
$Total\, number\, of\, countries = \sum Number\, of\, countries$

STEP 8

Now, divide the total sum by the total number of countries to get the best estimate of the average obesity percentage.
$Average\, obesity\, percentage = \frac{{Total\, sum}}{{Total\, number\, of\, countries}}$

STEP 9

Round the average obesity percentage to two decimal places.

STEP 10

To determine whether the obesity rate of the United States is above or below average, compare the obesity rate of the United States ( $33.9\%$ ) with the average obesity percentage.

STEP 11

STEP 12

Round the percentage to the nearest whole number.

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STEP 1

STEP 2

First, we need to find the midpoint of each range. The midpoint is the average of the lower and upper bounds of the range.Midpoint=Lower bound+Upper bound2Midpoint = \frac{{Lower\, bound + Upper\, bound}}{2}Midpoint=2Lowerbound+Upperbound​

STEP 3

Calculate the midpoints for each range.For the first range 11.−20.4511.-20.4511.−20.45, the midpoint isMidpoint=11.+20.452Midpoint = \frac{{11. +20.45}}{2}Midpoint=211.+20.45​Repeat this calculation for all other ranges.

STEP 4

Next, multiply each midpoint by the number of countries in that range.Product=Midpoint×Number of countriesProduct = Midpoint \times Number\, of\, countriesProduct=Midpoint×Numberofcountries

STEP 5

Calculate the products for each range.For the first range, the product isProduct=Midpoint×28Product = Midpoint \times28Product=Midpoint×28Repeat this calculation for all other ranges.

STEP 6

Add up all the products to get the total sum.Total sum=∑ProductTotal\, sum = \sum ProductTotalsum=∑Product

STEP 7

Calculate the total number of countries by adding up the number of countries in each range.Total number of countries=∑Number of countriesTotal\, number\, of\, countries = \sum Number\, of\, countriesTotalnumberofcountries=∑Numberofcountries

STEP 8

STEP 9

Round the average obesity percentage to two decimal places.

STEP 10

To determine whether the obesity rate of the United States is above or below average, compare the obesity rate of the United States (33.9%33.9\%33.9%) with the average obesity percentage.

STEP 11

STEP 12

Round the percentage to the nearest whole number.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

First, we need to find the midpoint of each range. The midpoint is the average of the lower and upper bounds of the range.
$Midpoint = \frac{{Lower\, bound + Upper\, bound}}{2}$

Calculate the midpoints for each range.
For the first range $11.-20.45$ , the midpoint is $Midpoint = \frac{{11. +20.45}}{2}$ Repeat this calculation for all other ranges.

Next, multiply each midpoint by the number of countries in that range.
$Product = Midpoint \times Number\, of\, countries$

Calculate the products for each range.
For the first range, the product is $Product = Midpoint \times28$ Repeat this calculation for all other ranges.

Add up all the products to get the total sum.
$Total\, sum = \sum Product$

Calculate the total number of countries by adding up the number of countries in each range.
$Total\, number\, of\, countries = \sum Number\, of\, countries$

To determine whether the obesity rate of the United States is above or below average, compare the obesity rate of the United States ( $33.9\%$ ) with the average obesity percentage.