In Google Analytics you can check the average PageSpeed of a website, as well as other speed metrics.
You can find the report in the category “content” under “website speed.”
When using the key values from Google Analytics, it is important keep a few things in mind. Google will take redirects into account when they calculate the average page load time and they will only calculate the website-speed for users whose browser is able to support the HTML5-interface “Navigation Timing” or those who have installed the Google Toolbar. This can be the reason why these key values may fluctuate or why they may be different compared to other evaluations