There are 15 students, thus, the median is represented by the $8^{th}$ student, who missed 2 days of school.  The mean is calculated by: $\frac{3 \times 0 + 1 \times 1 + 4 \times 2 + 3 \times 1 + 4 \times 1 + 5 \times 5}{15} = 2\frac{11}{15}$, making for a difference of $\frac{11}{15}\text{ days}$.
For the data whose frequency histogram is shown, by how many days is the mean number of days missed per student greater than the median number of days missed per student for the 15 students? Express your answer as a common fraction.

[asy]
draw((0,0)--(0,6),linewidth(2));
draw((0,0)--(6,0),linewidth(2));

draw((0,0)--(1,0)--(1,3)--(0,3)--(0,0)--cycle,linewidth(2));
draw((1,0)--(2,0)--(2,1)--(1,1)--(1,0)--cycle,linewidth(2));
draw((2,0)--(3,0)--(3,4)--(2,4)--(2,0)--cycle,linewidth(2));
draw((3,0)--(4,0)--(4,1)--(3,1)--(3,0)--cycle,linewidth(2));
draw((4,0)--(5,0)--(5,1)--(4,1)--(4,0)--cycle,linewidth(2));
draw((5,0)--(6,0)--(6,5)--(5,5)--(5,0)--cycle,linewidth(2));

draw((0,1)--(6,1),dashed);
draw((0,2)--(6,2),dashed);
draw((0,3)--(6,3),dashed);
draw((0,4)--(6,4),dashed);
draw((0,5)--(6,5),dashed);

label("0",(.5,0),S);
label("1",(1.5,0),S);
label("2",(2.5,0),S);
label("3",(3.5,0),S);
label("4",(4.5,0),S);
label("5",(5.5,0),S);

label("1",(0,1),W);
label("2",(0,2),W);
label("3",(0,3),W);
label("4",(0,4),W);
label("5",(0,5),W);

label("Number of School Days Missed",(2.5,8));
label("by Mr. Clark's Students",(2.5,7));

label("$\#$ of Days of School Missed",(3,-2));

label(rotate(90)*"$\#$ of Students",(-2,2));
[/asy]