The mean of a data set is the sum of the values in the data set divided by the number of values in the data set. The mean of 75 is obtained by finding the sum of the first 10 ratings and dividing by 10. Thus, the sum of the first 10 ratings was 750. In order for the mean of the first 20 ratings to be at least 85, the sum of the first 20 ratings must be at least (85)(20)=1700. Therefore, the sum of the next 10 ratings must be at least 1700 − 750 = 950. The maximum rating is 100, so the maximum possible value of the sum of the 12th through 20th ratings is 9×100=900. Therefore, for the store to be able to have an average of at least 85 for the first 20 ratings, the least possible value for the 11th rating is 950−900=50.