To find the missing value in the two-way frequency table, we can use the information provided in the total column for the different grade levels.
Let's denote the missing value for middle school students who like pickles as \( x \).
From the table, we know the following:
- The total number of middle school students is 100.
- The total number of middle school students who do not like pickles is 8.
- Therefore, the total number of middle school students who like pickles can be calculated with the equation:
\[ \text{Total Middle School Students} = \text{Middle School Students Who Like Pickles} + \text{Middle School Students Who Do Not Like Pickles} \]
Substituting the known values into this equation gives:
\[ 100 = x + 8 \]
Now, we can solve for \( x \):
\[ x = 100 - 8 \] \[ x = 92 \]
Thus, the missing value for middle school students who like pickles is \( 92 \).
Now, let's check the total of students who like pickles across all grade levels:
- Elementary School Students who like pickles: 85
- Middle School Students who like pickles: 92 (the value we just found)
- High School Students who like pickles: 97
Calculating the total:
\[ 85 + 92 + 97 = 274 \]
This matches the total provided for students who like pickles.
Therefore, the completed and verified missing value is:
92.