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For the data whose frequency histogram is shown, by how many days is the mean number of days missed per student greater than the mode number of days missed per student for the 15 students? Express your answer as a common fraction.

Apr 3, 2021

There is a total of $3+1+4+1+1+5=15$ total students, and getting the total number of days missed is $0*3+1*1+2*4+3*1+4*1+5*5=0+1+8+3+4+25=41$ total days missed. This means the average days missed is $\frac{41}{15}=2$ $\frac{11}{15}$. The mode number of days missed is 5, because the most common number of days missed was 5. What I don't understand is that the mean is LESS than the mode, not GREATER than the mode. So the absolute difference between them would be $|5-2$ $\frac{11}{15}|=2$ $\frac{4}{15}$, or, as a common fraction, $\boxed{\frac{34}{15}}$