Video Transcript
The following table shows the ages
of people applying for a job, knowing that no one is older than 50 years. Which of the following is the
cumulative frequency graph? Options (A), (B), (C), (D), and
(E).
In this question, we are given a
grouped frequency table showing the ages of all of the applicants to a job. And we want to use this table to
identify the correct cumulative frequency graph. We could do this by eliminating
options. However, we are going to answer
this question by sketching the cumulative frequency graph since this is a useful
skill.
To begin, let’s clear the options
from the screen. We can then recall that the
cumulative frequency is the running total of the frequencies. This means that we can find the
cumulative frequency in the table by finding the sum of all of the previous
frequencies. The frequency of the first group is
two, so the cumulative frequency in this column is two. We need to add this to the next
frequency of five to find the next cumulative frequency. We can then calculate that five
plus two is seven. We then add the previous cumulative
frequency of seven onto the next frequency of 10 to see that the next cumulative
frequency is 17.
We continue this process to fill in
all of the cumulative frequencies in the table. It is worth noting that the final
cumulative frequency must be equal to the total number of applicants, in this case,
69. We can now recall that to draw the
cumulative frequency graph of the data in the table, we need to plot points with
𝑥-coordinates equal to the upper bounds of the classes and the corresponding
𝑦-coordinates equal to the cumulative frequency.
To do this, we can note two
things. First, no applicant is older than
50, so we can choose an upper bound of 50 for the final class. Similarly, no applicant is younger
than 19, so we can start our graph at 19 with a frequency of zero. Choosing the upper bounds and the
cumulative frequencies gives us the following points that we want to plot.
We now need to sketch the axes of
our graph. The 𝑥-axis is the ages of the
applicants, and the 𝑦-axis will be the cumulative frequency. We then plot each of the
points. And since the options are connected
with straight lines, we will connect these points with straight lines as shown. We can see that this matches the
graph given in option (E).
