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.
[tex]\begin{gathered} S_7=49+63=112 \\ S_8=58+51=109 \end{gathered}[/tex]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.
[tex]\begin{gathered} S_{-5}=49+58=107 \\ S_{+5}=51+63=114 \end{gathered}[/tex]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.
[tex]\begin{gathered} \frac{58}{109}=0.532\cdot100=53.2 \\ \frac{51}{109}=0.468\cdot100=46.8 \end{gathered}[/tex]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.
[tex]S_7=49+63=112[/tex]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.
