Because the number with the highest frequency in this set of data is 63, 63 is the mode of this set of data;

Arrange this set of data in descending order: 60, 63, 63, 63, 68, 69, 74, 76, 77, 87, so the median is: (68+69) ÷ 2 = 68.5;

Range: 87-60 = 27;

The average value is: (87+77+76+74+69+60+68+63+63) ÷10 = 70.

So their mode, median, range and average in this set of data are 63, 68.5, 27 and 70 respectively.