single shape layer with Repeater effect: is it possible to randomly spread out the Repeater copies?

Thank you so much Mylenium, Gutterfish, Roland, and Rick, for your help. Gutterfish I'll definitely take a close look at your program, as I may need to do this type of effect quite often with future infographics, and it looks like Pastiche could save me a lot of time. Thanks again everyone.   

See if this does what you want -

All good options from Mylenium and GTF. I'll add AE's built-in particle generator, Particle Playground to the list of effects that allows you to place an image/video into a grid. You can then use a greyscale image to offset elements in the grid to create randomness.

I would use a plugin I own called Pastiche (Search results for: 'pastiche' - aescripts + aeplugins - aescripts.com​ ) for this but for a one time thing just randomize 10 layers then pre compose them.  Duplicate the composition as many times as you want and flip half of them by changing the X Scale to a negative value...I think ALT+Home is the shortcut. Arrange them and add a few individual layers to fill in any gaps if needed.  Again if this is a "one time" or even "once in a while" thing then the most economic solution is to do it by hand.

If it's something you do enough to have it start cutting into your bottom line then invest in Form like Myll said or check out Pastiche

or (if money isn't a problem) check out Motion Boutique's Motion Bundle which comes with Newton 3, Pastiche & Layer Generator. 

Nothing missing. That's just how it works. If you need different patterns, you need to use other tools like grid-based particle tools such as Trapcode Form or even AE's good old own Card Dance - it will just take time to understand those tools and how to get the most out of them e.g. using custom parameter maps.

Mylenium