The table shows the number of days taken off work by 40 workers in a year. By constructing a frequency table or otherwise, calculate the number of workers who
took 20 or more days off work.
The data values in the table represent the number of days absence taken by 40
workers. If we consider the range of data in the table, the smallest value is five and the
highest value is 30. If we were to create a frequency table to represent every individual data value from
five to 30, the table would be very large. As such, we will create a grouped frequency table. The top row of our table will be the number of days absent and the bottom row will be
the frequency, that is, the number of people, in each group.
When creating a grouped frequency table, we must ensure that classes are
exhaustive. There should be a class for every data value in the set. The classes should also be mutually exclusive. There should be no overlapping data values between classes. Finally, the classes should be continuous. There should be no gaps between the classes. In this question, we will use four groups: zero to nine, 10 to 19, 20 to 29, and 30
to 39 days absent. Note that we must ensure that 20 is the lower bound of one of the groups to answer
We can see from the table that there were six workers who took between zero and nine
days off work. This means that the first frequency is six. Next, we see that there are 15 workers that took between 10 and 19 days off work. The third frequency is 17, since 17 workers had between 20 and 29 days absence. Finally, since two workers took 30 days off work, the frequency in the last group is
two. At this stage, it is worth noting that six plus 15 plus 17 plus two equals 40, which
is equal to the total number of workers in the table.
Returning to the question, we need to calculate the number of workers who took 20 or
more days off work. This corresponds to the last two columns in the table. 17 plus two equals 19. We can therefore conclude that 19 workers took 20 or more days off work.