You first have to convert your dates to date numbers (using the datenum function). Then use that as your x-coordinate (independent variable) in your plot, and use the datetick function to format the date numbers as date strings.
This should get you started:
x = {'July 15'; 'Aug 15'; 'Sept 15'; 'Oct 15'; 'Nov 15'; 'Dec 15'; 'Jan 16'; 'Feb 16'; 'Mar 16'; 'April 16'; 'May 16'};
xdn = datenum(x); % Use This For ‘x’
xds = datestr(xdn, 'mmm yy') % Check Conversion (Not Necessary For Code)
I had to convert your dates to a cell array of strings. See: Cell Arrays for details. See the documentation for times and dates as well.
I leave the rest to you.
