# Predicting binary outcomes for observations given statistics on binned data

SAT Verbal scores range from 200 to 800 in increments of 10. MIT says that for the class of 2023, the acceptance rates were, for various score ranges

• 750-800 10% = 677/6504
• 700-740 06% = 312/5039
• 650-690 03% = 87/2614
• 600-640 01% = 11/1091
• 200-590 00% = 3/688

How would you estimate the probability of acceptance for a given score, say 750, given this data? You could say 10%, but in reality the probability is likely lower for scores of 750 than 800. You can fit smooth monotonic functions to acceptance rate vs score to the binned data, but there is no unique solution.

• Percentages provided are only approximate: You might use $(677+312)/(6504+5039) = 0.0857.$ So maybe say about 8%. Fitting a smooth curve to all the data may not be helpful. Because you don't know what other relevant criteria are correlated with SAT verbal scores. Nov 20 '19 at 6:46