Let's analyze the table to find the total number of students polled and calculate the mean.
The given table lists the number of candies each student has, with some values missing (represented by empty cells).
Here is the table for reference:
| Row | Candies |
|-----|-------------------------------------------|
| 1 | 7 |
| 4 | 1, 1, 2, 9 |
| 5 | 3, 3, 3, 3, 3 |
| 6 | 1, 3, 4, 6, 7, 8, 9 |
| 7 | 1, 3, 5, 5, 7 |
| 8 | 2, 2, 3, 4 |
To get the total number of students polled, we need to count each individual entry that is not missing:
Step 1: Determine the number of students polled.
- Row 1: 1 student ([7])
- Row 4: 4 students ([1, 1, 2, 9])
- Row 5: 5 students ([3, 3, 3, 3, 3])
- Row 6: 7 students ([1, 3, 4, 6, 7, 8, 9])
- Row 7: 5 students ([1, 3, 5, 5, 7])
- Row 8: 4 students ([2, 2, 3, 4])
```
Total number of students: 1 + 4 + 5 + 7 + 5 + 4 = 26 students polled.
```
Step 2: Flatten the data and calculate the total sum of candies.
- Row 1: [7]
- Row 4: [1, 1, 2, 9]
- Row 5: [3, 3, 3, 3, 3]
- Row 6: [1, 3, 4, 6, 7, 8, 9]
- Row 7: [1, 3, 5, 5, 7]
- Row 8: [2, 2, 3, 4]
Collect all the numbers together:
[tex]\[ 7, 1, 1, 2, 9, 3, 3, 3, 3, 3, 1, 3, 4, 6, 7, 8, 9, 1, 3, 5, 5, 7, 2, 2, 3, 4 \][/tex]
Sum up all the candies:
[tex]\[ 7 + 1 + 1 + 2 + 9 + 3 + 3 + 3 + 3 + 3 + 1 + 3 + 4 + 6 + 7 + 8 + 9 + 1 + 3 + 5 + 5 + 7 + 2 + 2 + 3 + 4 = 98 \][/tex]
Step 3: Calculate the mean and round it to the nearest cent (hundredths).
[tex]\[ \text{Mean} = \frac{\text{Sum of all candies}}{\text{Total number of students}} = \frac{98}{26} \approx 3.77 \][/tex]
So, the total number of students polled is 26, and the mean number of candies to the nearest cent is 3.77.
Final Answers:
a. How many students were polled? \(\boxed{26}\)
b. Find the mean to the nearest cent. [tex]\(\boxed{3.77}\)[/tex]
