- For use of ˛tabularx
package you should define
\textwidthof page layout, for example with option
varwidth=34em`
tabularx
table should have at least one X
or from it derived column type
with new column, your table have 8 columns, but you define 0 (without new column).
- it is not entirely clear how column headers should be. So I add one
\cline
below multi column cell:
\documentclass[margin=3mm, varwidth=34em]{standalone}
\usepackage{multirow, tabularx}
\newcolumntype{C}{>{\centering\arraybackslash}X}
\begin{document}
\setlength\tabcolsep{4pt}
\begin{tabularx}{\linewidth}{@{} c c CCCCC c @{}}
& & \multicolumn{5}{c}{N} & \\
\cline{3-7}
& W & 7 & 9 & 13 & 17 & 19 & 1 \\
\hline
\multirow{10}{*}{S}
& 0.6078 & 1.0592 (4) & 1.0646 (4) & 1.0647 (6) & 1.0647 (5) & 1.0647 (5) & 1.0647 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
\end{tabularx}
\end{document}

Addendum:
Withtblr
of tabularray
package you can write a bit more fancy (easy to read) table with c
columns (similar as is used in @Pieter van Oostrum answer) with grouping of rows:
\documentclass[margin=3mm]{standalone}
\usepackage{tabularray}
\begin{document}
\begin{tblr}{colsep=4pt,
colspec={@{} *{8}{c} @{}},
rowsep=1pt,
row{even[3]} = {belowsep=1ex}
}
& & \SetCell[c=5]{c} N
& & & & & \\
\cline{3-7}
tip & W & 7 & 9 & 13 & 17 & 19 & 1 \\
\hline
\SetCell[r=10]{c} S
& 0.6078 & 1.0592 (4) & 1.0646 (4) & 1.0647 (6) & 1.0647 (5) & 1.0647 (5) & 1.0647 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
& 1.0012 & 1.1614 (7) & 1.1666 (4) & 1.1668 (6) & 1.1668 (5) & 1.1668 (5) & 1.1668 \\
\end{tblr}
\end{document}

\begin{tabularx}{\textwidth}{c ccc c cccc}
is wrong, use a standard tabular or use an X columntexdoc tabularx
the only thingtabularx
does is achieve a specfied table width by adjusting the widths of X columns. You only have c columns so the package can do nothing useful