Question

The table shows the results of a random survey of students in grade 7 and grade 8. Every student surveyed gave a response. Each student was asked if they exercised 5 or more hours last week or less than 5 hours last week. Based on the results of the survey, which statement is true?A. More grade 8 students were surveyed than grade 7 students.B. More than 50% of the students surveyed exercised less than 5 hours last week.C. Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week.D. A total of 107 grade 7 students were surveyed.

Answer 1

Based on the analysis above, the correct statement is:

C. Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week.

Determining the true statement

Based on the given table, analyze the statements:

A. More grade 8 students were surveyed than grade 7 students.

This statement cannot be determined solely based on the information provided. We don't have the total number of students surveyed for each grade, so we cannot compare the sample sizes.

B. More than 50% of the students surveyed exercised less than 5 hours last week.

To determine if more than 50% of the students surveyed exercised less than 5 hours, compare the total number of students who exercised less than 5 hours to the total number of students surveyed.

Adding the values for grade 7 and grade 8 students who exercised less than 5 hours (49 + 58 = 107), and adding the values for grade 7 and grade 8 students who exercised 5 or more hours (63 + 51 = 114), we can see that 107 out of 221 students surveyed exercised less than 5 hours. Therefore, the statement is false. Less than 50% of the students surveyed exercised less than 5 hours.

C. Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week.

To determine if less than 50% of the grade 8 students exercised 5 or more hours, compare the number of grade 8 students who exercised 5 or more hours (51) to the total number of grade 8 students surveyed (51 + 58 = 109). Since 51 out of 109 is less than 50%, the statement is true. Less than 50% of the grade 8 students surveyed exercised 5 or more hours.

D. A total of 107 grade 7 students were surveyed.

Based on the given information, we know that 49 grade 7 students exercised less than 5 hours and 63 grade 7 students exercised 5 or more hours. The total number of grade 7 students surveyed is the sum of these values, which is 49 + 63 = 112. Therefore, the statement is false. A total of 107 grade 7 students were not surveyed.

Based on the analysis above, the correct statement is:

C. Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week.

Answer 2

We have a table of results about a survey, from this we must determine which statement is correct, For this, we will analyze them one by one.

A. More grade 8 students were surveyed than grade 7 students.

To find that out, let's add up the results of all the students surveyed for grade 7 and all the students surveyed for grade 8.

`\begin{gathered} S_7=49+63=112 \\ S_8=58+51=109 \end{gathered}`

There are more grade 7 students surveyed, in conclusion, this statement is incorrect.

B. More than 50% of the students surveyed exercised less than 5 hours last week.

To find this data, we must add up all the students who exercised less than 5 hours and those who exercised 5 hours or more and compare the data.

`\begin{gathered} S_(-5)=49+58=107 \\ S_(+5)=51+63=114 \end{gathered}`

Less than 50% of the students surveyed exercised less than 5 hours last week, in conclusion, his statement is incorrect.

C. Less than 50% of the grade 8 students surveyed exercised 5 or more hours last week.

To determine if this is true, we look at the survey of grade 8 students, we use the sum total of these students and divide each group by the total number, then multiply by 100 to find the percentages for comparison.

`\begin{gathered} (58)/(109)=0.532\cdot100=53.2 \\ (51)/(109)=0.468\cdot100=46.8 \end{gathered}`

There is a lower percentage at 50% of the grade 8 students surveyed exercised 5 or more hours last week, in conclusion, his statement is correct.

D. A total of 107 grade 7 students was surveyed.

Let's remember that we already did the sum of all the students in grade 7.

`S_7=49+63=112`

We see that the grade 7 respondents are more than 107 students, in conclusion, his statement is incorrect.

Finally, out of all the statements, the only correct option is option C.