To determine the average rating of the documentary based on the students' ratings provided, we can use the information that some students scored below the average (negative values) and others scored above the average (positive values).
Let's denote the average rating of all students as \( A \).
From the table:
- Jennifer: \( A - 12 \) (rating = A - 12)
- Braden: \( A + 5 \) (rating = A + 5)
- Alexandra: \( A + 8 \) (rating = A + 8)
- Christina: \( A - 6 \) (rating = A - 6)
- Franco: \( A - 1 \) (rating = A - 1)
To find the average rating \( A \), we can calculate the overall rating of each student, then consider all ratings together to find the average.
The total ratings can be calculated as follows:
\[ \text{Total Ratings} = (A - 12) + (A + 5) + (A + 8) + (A - 6) + (A - 1) \]
Simplifying the total:
\[ \text{Total Ratings} = 5A - 12 + 5 + 8 - 6 - 1 \] \[ \text{Total Ratings} = 5A - 6 \]
The number of students is 5, so the average rating \( A \) can be expressed as:
\[ A = \frac{5A - 6}{5} \]
Now multiply both sides by 5 to eliminate the fraction:
\[ 5A = 5A - 6 \]
This shows that the equation holds true for any value of \( A \). However, this isn't very helpful without knowing further information about the ratings and their calculations.
We can also note from the individual ratings:
- The total deviation from the average ratings for Jennifer, Christina, Franco (who rated below the average) sums up to -12 - 6 - 1 = -19.
- The total deviation for Braden and Alexandra (who rated above the average) sums up to +5 + 8 = +13.
Thus, total deviations equal -19 + 13 = -6.
To calculate the average rating,
The total deviation indicates that the average itself shifts slightly higher in calculation, considering the sums of their individual scores.
If we set the sum of deviations equal to a determinate rating for calculation, we would need additional specific ratings or information to fully derive a concrete average.
Would you like to make certain assumptions or provide further information to calculate a clear average?