Hi lass..
According to the 1900 US census
Firtchburg, Ward 2, Worcester, MA
The MCKENZIE children of Kenneth and Sarah were:
Alexander, 11, b Dec 1888, Rhode Island
Margaret, 9, b Dec 1890, Rhode Island
Annie, 7, b Oct 1892/3 (very faint), Rhode Island
Kenneth, 5, b Jan 1895, Rhode Island
Sadie, 3, b Mar 1897, MA
Thomas, 1, b May 1899, MA
Seems to match the October date in your post.
The census was taken 2 July 1900, and Question was: (What was your) Age last birthday?
Hope this helps.
Grub