Question

to learn about budgets, the students in ms. hendersons classes are each planning a dream vacation to a south american country. the graph below shows the relative frequency of each country the students chose. dream vacation select all of the statements that describe the data. the mode of the data is ecuador. the students are planning vacations to exactly 5 different countries. more than half of the students chose ecuador or peru. less than a quarter of the students chose brazil.

Explanation:

Step1: Understand the mode

The mode is the value with the highest frequency. In the bar - graph, Ecuador has the highest relative frequency. So, "The mode of the data is Ecuador" is correct.

Step2: Count the number of countries

Count the number of bars in the bar - graph. There are 6 bars corresponding to 6 countries (Argentina, Brazil, Chile, Ecuador, Peru, Venezuela). So, "The students are planning vacations to exactly 5 different countries" is incorrect.

Step3: Calculate the sum of Ecuador and Peru's frequencies

Add the relative frequencies of Ecuador and Peru. Let \(f_{Ecuador}=25\%\) and \(f_{Peru} = 20\%\). Then \(f_{Ecuador}+f_{Peru}=25\% + 20\%=45\%\lt50\%\). So, "More than half of the students chose Ecuador or Peru" is incorrect.

Step4: Check Brazil's frequency

Brazil's relative frequency is \(20\%\). Since \(\frac{1}{4}=25\%\) and \(20\%\lt25\%\). So, "Less than a quarter of the students chose Brazil" is correct.

Answer:

The mode of the data is Ecuador; Less than a quarter of the students chose Brazil.