3 perfect scores of 10
There can't be 5x10 because the mode (the commonest score) is 7. Hence if there are 5x10 there must be 6 x7, but the median (the middle score) is 8 and this would make at least 12 scores which is impossible.
There can't be 4x10. If there were 4 x10 there would be 5x7 (7=mode), 1x8(median) + either another 8 or 9. Assuming the best case scenario (2 x8). The total of the 11 scores = 91. They should add up to 88 (mean = 8, (11x8=88)
If there are 3x10, there must be at least 4x7(mode =7), 3more 8+(median = 8), and 1 x less than 7.
3x10, 3x8, 4x7 and 1x6 fits the bill.
Mean= (30+24+28+6)/11 = 88/11 = 8 OK
Median is the sixth number in the series = 8 OK
The mode is the commonest number. Mode = 7 OK
