ai) The mode is the most frequent number in the data set, in this case it is 0 days (16 students), answer: 0

aii) The median is the number the appears in the middle when all the numbers are written out in a line.

16 zeros, 5 ones, 7 twos, 2 threes, 1 four, 1 five

00000000000000001111122222223345

The median is 0.5 (in between 0 and 1)


b) The mean is just the average, the average number of days that the students were absent in this case.
[16(0)+5(1)+7(2)+2(3)+4(1)+5(1)]÷32=1.0625


c) The probability that the student was absent for more than 2 days is just the number of numbers in the data set that are greater than 2, divided by the total number.

There are 32 numbers in this set
(16 zeros, 5 ones, 7 twos, 2 threes, 1 four, 1 five)
Only 4 of them are greater than 2 (two 3s, one 4, one 5), so the probability of getting a number greater than 2 is,
4÷32=0.125 or 12.5%
Answer: 12.5%