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According to the documentation of quantile it takes an optional argument named type which is an integer from 1 to 9. These correspond to different algorithms for calculating quantiles; the default is algorithm 7. You will have to find out which one corresponds to the lecture; my guess is type 5.

sage: r.quantile([89, 90, 86, 96, 84, 100, 85, 96, 88, 89], type=5)
  0%  25%  50%  75% 100% 
  84   86   89   96  100