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A questionnaire was given to students in an introductory statistics class during the first week of the course. One question asked, "How stressed have you been in the last [tex]$2 \frac{1}{2}$[/tex] weeks, on a scale of 0 to 10, with 0 being not at all stressed and 10 being as stressed as possible?" The students' responses are shown in the frequency distribution below. How many students were involved in the study?

Frequency Distribution

\begin{tabular}{|c|c|}
\hline
Stress Rating & Frequency \\
\hline
0 & 6 \\
\hline
1 & 3 \\
\hline
2 & 4 \\
\hline
3 & 11 \\
\hline
4 & 14 \\
\hline
5 & 20 \\
\hline
6 & 15 \\
\hline
7 & 29 \\
\hline
8 & 31 \\
\hline
9 & 10 \\
\hline
10 & 16 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To determine the total number of students who participated in the study, you need to sum up the frequencies for each stress rating. Here is the step-by-step solution:

1. List out the stress ratings and their corresponding frequencies from the given frequency distribution:

- Stress Rating 0: 6 students
- Stress Rating 1: 3 students
- Stress Rating 2: 4 students
- Stress Rating 3: 11 students
- Stress Rating 4: 14 students
- Stress Rating 5: 20 students
- Stress Rating 6: 15 students
- Stress Rating 7: 29 students
- Stress Rating 8: 31 students
- Stress Rating 9: 10 students
- Stress Rating 10: 16 students

2. Add up all the frequencies to find the total number of students involved in the study:

[tex]\[ 6 + 3 + 4 + 11 + 14 + 20 + 15 + 29 + 31 + 10 + 16 \][/tex]

3. Perform the addition step by step:

[tex]\[ 6 + 3 = 9 \][/tex]
[tex]\[ 9 + 4 = 13 \][/tex]
[tex]\[ 13 + 11 = 24 \][/tex]
[tex]\[ 24 + 14 = 38 \][/tex]
[tex]\[ 38 + 20 = 58 \][/tex]
[tex]\[ 58 + 15 = 73 \][/tex]
[tex]\[ 73 + 29 = 102 \][/tex]
[tex]\[ 102 + 31 = 133 \][/tex]
[tex]\[ 133 + 10 = 143 \][/tex]
[tex]\[ 143 + 16 = 159 \][/tex]

4. Therefore, the total number of students involved in the study is [tex]\(159\)[/tex].