The total number of pairs of shoes owned by the 6th graders surveyed is 2*5 + 3*6 + 4*1 + 5*1 + 6*4 + 7*7 + 8*2 + 10*1 = 24 + 18 + 4 + 5 + 24 + 49 + 16 + 10 = 150.
The total number of 6th graders surveyed is 5 + 6 + 1 + 1 + 4 + 7 + 2 + 1 = 27.
Therefore, the mean number of pairs of shoes owned by the 6th graders surveyed is 150 / 27 = 5.56.
Rounding to the nearest whole number, the mean number of pairs of shoes owned by the 6th graders surveyed is 6 pairs of shoes.