What version of InDesign are you using? If you have InDesign CS6 or later, you can either use Edit > Place and Link, or the Content Collector/Content Placer tools with the Link option turned on. Either of those tools/commands take the "parent" objects and makes linked copies of it. When changes occur in the parent object, you have the option of updating the "child" copies.
I'm using InDesign CC. Before I can place it, don't I have to somehow export/save my selection. I've tried using the snippets and the content collector and the library, but it's not working to just update the one element which then updates the "children". What could I be doing wrong?
You don't need to export/save your selection when you're using the Content Collector/Placer tools. Here's the workflow:
(1) Create the table in one text frame and place it on the first page. This is the parent frame.
(2) Choose the Content Collector tool. This is the fifth tool down on the Tools, and its icon has an arrow pointing down and right. Move over the parent frame and it's highlighted.
When you click it's added to the Conveyor which appears automatically. (You could add other objects as well if you wanted to copy them.)
(2) Move over the second page. Switch to the Content Placer tool (icon arrow points up and right). You should turn on two options on the Conveyor: Click Create Link. Choose the middle icon of three in the center of the Conveyor so you can place the same object multiple times. (Otherwise, it drops it and moves to the second item in the Conveyor.) Click to place on the second page.
Repeat placing the frame on each other page. Now, all the copies of the table frame are all linked to the parent frame.
(3) When it's time to edit the tables, edit the copy on the first page (the parent):
Now, when you view each of the child table frames, you'll see a warning icon which lets you know the parent frame has changed:
You could click the icon on the child frame on page 2, and it would be changed. To update all the child frames go to the Links panel. You'll see each instance of the child frame showing the yellow warning. To update them all, Option/Alt click the Update Link icon.