The following table shows the ages
of people applying to a company. What are the missing values from
the cumulative frequency table respectively?
In this question, we are given a
grouped frequency table of the ages of people applying to a job. And we want to find the missing
values in the table. To do this, we can start by
recalling that the cumulative frequency is the running total of the frequencies. This means that we can calculate
the cumulative frequency by adding all of the previous frequencies together.
The first cumulative frequency is
just equal to the frequency in the first group, which is two. If we wanted to calculate the
cumulative frequency in the second group, we would need to add the frequency of five
onto the previous cumulative frequency to obtain five plus two equals seven. Of course, we are already given
that the cumulative frequency in this group is seven.
We can follow the same process for
the missing entries. In the third group, we need to add
its frequency of 10 onto the previous cumulative frequency of seven, which we can
calculate is equal to 17. For the next missing entry, we add
the frequency of 12 onto the previous cumulative frequency of 31 to get 43. For the final cumulative frequency,
there are two ways that we can find its value. Either we can use the fact that the
final cumulative frequency is always equal to the total population to see that it is
equal to 69. Or we can follow the same process
we did before to add the frequency of seven onto the previous cumulative frequency
of 62 to get 69.
Hence, the missing values from the
cumulative frequency table in order are two, 17, 43, and 69.