We start with the given equations:

\(\Sigma(x - 200) = 446\)

\(\Sigma x = 6846\)

We can express \(\Sigma(x - 200)\) as:

\(\Sigma x - \Sigma 200 = 446\)

Since \(\Sigma 200 = 200n\), we substitute:

\(\Sigma x - 200n = 446\)

Substitute \(\Sigma x = 6846\) into the equation:

\(6846 - 200n = 446\)

Solve for \(n\):

\(6846 - 446 = 200n\)

\(6400 = 200n\)

\(n = \frac{6400}{200}\)

\(n = 32\)