Eighty candidates took an examination in Astronomy, for which no candidate scored more than 80%. The examiners suggest that five grades, A, B, C, D and E, should be awarded to these candidates, using upper grade boundaries 64, 50, 36 and 26 for grades B, C, D and E, respectively. In this case, grades A, B, C, D and E, will be awarded in the ratio 1: 3 : 5 : 4 : 3.

a. Using the examiners’ suggestion, represent the scores in a cumulative frequency polygon and use it to estimate the median score.

b. All of the grade boundaries are later reduced by 10%. Estimate how many candidates will be awarded a higher grade because of this.