I have been working to increase my shop speed and have been using PageSpeed Insights to get an idea of what I need to work on. I have bit by bit making some progress, but I am getting frustrated tracking if my changes are actually even making a difference (or alas, making things worse!). When I run the test several times in a row I can at times get pretty different scores (plus or minus 10 points).
Hi @GriffCat, Shopify itself doesn't need jQuery (an old and outdated JS library), but some of the apps you use might depend on it.
If you want to remove it, you'd have to figure out what app needs it? Or maybe your theme?
The reason behind the speed fluctuation is because PageSpeed insights analyzes the page each time you load it. It could be the script is sometimes cached, sometimes isn't, it's a bit hard to see behind the scenes but fluctuations are normal.
Hope it helps. If you still have any questions drop me a message.