To find the mean number of hours spent on math homework, we first need to calculate the total hours spent by all students and then divide that by the total number of students.
Step 1: Calculate total hours spent by all students.
The data is as follows:
- 1 hour: 8 students
- 2 hours: 6 students
- 3 hours: 4 students
- 4 hours: 2 students
- 5 hours: 1 student
Now we calculate the total hours for each category and then sum them:
-
For 1 hour:
\(1 \text{ hour} \times 8 \text{ students} = 8 \text{ hours}\) -
For 2 hours:
\(2 \text{ hours} \times 6 \text{ students} = 12 \text{ hours}\) -
For 3 hours:
\(3 \text{ hours} \times 4 \text{ students} = 12 \text{ hours}\) -
For 4 hours:
\(4 \text{ hours} \times 2 \text{ students} = 8 \text{ hours}\) -
For 5 hours:
\(5 \text{ hours} \times 1 \text{ student} = 5 \text{ hours}\)
Now we sum these total hours:
\[ 8 + 12 + 12 + 8 + 5 = 45 \text{ total hours} \]
Step 2: Calculate total number of students.
Now we sum up the total number of students:
\[ 8 + 6 + 4 + 2 + 1 = 21 \text{ students} \]
Step 3: Calculate the mean number of hours.
Now we find the mean number of hours spent on math homework by dividing the total number of hours by the total number of students:
\[ \text{Mean} = \frac{\text{Total hours}}{\text{Total students}} = \frac{45 \text{ hours}}{21 \text{ students}} \approx 2.14 \text{ hours} \]
Thus, the mean number of hours students spent on math homework is 2.14 hours.