It would be best if you are a site administrator if you want to try out the following steps.

1. Log into your Moodle site.
2. Go to any course page.
3. Click "Turn editing on".
4. Click "Add an activity or resource".
5. Select "Quiz" and click "Add".
6. On the "Adding a new Quiz" page, put anything next to "Name" and click "Save and return to course"
7. On the course page, click the quiz that you created.
8. Click "Edit quiz".
9. Click "Add" under "Shuffle", and click "a new question".
10. Select "Essay" and click "Add".
11. Put anything next to "Question name" and anything next to "Question text".
12. Click "Save changes".
13. Go back to the course page.
14. Click "Switch role to..." in the "ADMINISTRATION" block, and click "Student".
15. Click the quiz that you just created.
16. Click "Attempt quiz now".
17. Put anything in the textbox as a response to the essay question.
18. Click "Next".
19. Click "Submit all and finish", twice.
20. Click "Re-attempt quiz".
21. Put anything in the textbox as a response to the essay question.
22. Click "Next".
23. Click "Submit all and finish", twice.
24. Do steps 20-23 four times.
25. Click "Return to my normal role" under "Switch role to..." in the "ADMINISTRATION" block.
26. Click "Results" under "Quiz administration" in the "ADMINISTRATION" block, and click "Manual grading".
27. Click "grade all" under "Total" on the "Questions that need grading" page.
28. "Attempts to grade" should be set to All (6), "Questions per page" should be set to 5 and "Order attempts" should be set to Randomly.
29. Click "Change options".
30. Click "Save and go to next page".
31. The page should have been reloaded.

As you can see, the page reloads, instead of you going to the next page. You should go to the next page. I know it's a random order, and going to the same page is practically the same thing. However, this causes confusion with users who expect to see a list of pages to navigate to when "Order attempts" is set to Randomly, but there is no list of pages, as they would see the list of pages when "Order attempts" is set to By date.