I presume this is your site? Your design has a serious flaw: the number "1" is "selected" when you first view the page, which biases the results. You apparently tried to "fix" this by forcing the user to move the slider before the choice would be accepted, but that also biases the results.
The only way to really make it unbiased is with a text box. The next best thing would have been ten buttons in a row (but then you would have had to make sure that they didn't go off the right side of the screen).
I'd actually be interested in how different ways of presenting the choice affect the number chosen. It would be interesting of the author ran an A/B test with different methods of selection (text box, row of buttons 1-10, row of buttons in random order, slider, etc) to see what the differences would be.
The only way to really make it unbiased is with a text box. The next best thing would have been ten buttons in a row (but then you would have had to make sure that they didn't go off the right side of the screen).