The following data was collected from the titration of an unknown concentration of HCl with 1.0 mol/L NaOH using phenolphthalein as the indicator. The initial volume of HCl is 25.0 mL

This is just the chart that came with the question...

Volume of NaOH (mL) Observations
0.0 ------------------------- clear
5.0-------------------------- clear
10.0 ------------------------ clear
15.0 ------------------------ clear
20.0 ------------------------ clear
22.5 ------------------------ some pink but clears upon mixing
25.0 ------------------------ solution staying pink
27.5 ------------------------ pink
30.0 ------------------------ pink
35.0 ------------------------ pink
40.0 ------------------------ pink
45.0 ------------------------ pink
50.0 ----------------------- pink

How do you determine the volume of NaOH at the equivalence point? Thanks!

The equivalence point is, obviously, the point at which the solution changes color. Phenolphthalein is colorless in acidic solution, but changes to a pink in basic solution. 22.5 mL cleared upon mixing -- so the base reacted -- it's still acidic. At 25.0 mL, the solution is staying pink. That would be past the equivalence point.

I'm surprised at the difference between "22.5 -- some pink but clears upon mixing" and "25.0 - solution staying pink". That's 2.5 mL apart -- a very large difference for a titration. Usually, you can get within 1 drop (0.05 mL) and often 1/2 drop (one touches off the "half drop" and swirls the flask's contents to pick up the liquid). The real equivalence point would be between 22.5 and 25.0 -- and probably closer to 22.5 mL than 25.0 mL. In my experience, it would probably be 22.6 mL.

If you had the pH of the solution, you could graph the change in pH. It would look something like the attachment (this isn't real data).