Video Transcript
The times, in seconds, for adults
to complete a puzzle were recorded. The results are given in the table
below. Which of the following is the
descending cumulative frequency diagram that represents this data? Is it option (A), (B), (C), (D), or
(E)?
The frequency table gives the times
in groups. For example, zero dash represents a
time of zero seconds or more up to but not including 30 seconds, since this is the
lower boundary of the next class. The descending cumulative frequency
for any value 𝑥 gives us the frequency of the values that are greater than or equal
to 𝑥. In order to draw a descending
cumulative frequency diagram, we first need to determine the descending cumulative
frequency values. We will add an extra row to our
table to help do this.
The first descending cumulative
frequency is always the total frequency. We can calculate this by adding the
frequencies three, 17, 35, 43, and two. This is equal to 100. In the context of this problem,
this means that 100 adults took a time of zero seconds or more to complete the
puzzle.
The second descending cumulative
frequency represents the number of adults who took 30 seconds or more to complete
the puzzle. This is equal to 100 minus three,
since we do not count the three adults in the first group who took less than 30
seconds to complete it. 100 minus three is equal to 97.
We can then repeat this process to
calculate the third descending cumulative frequency. This is equal to 97 minus 17 and
represents the number of adults who completed the puzzle in a time of 60 seconds or
more. The third descending cumulative
frequency is therefore equal to 80.
Continuing this process, we find
two further descending cumulative frequency values of 45 and two. It is common to include a final
descending cumulative frequency of zero. To do this, we recognize that there
are zero adults recorded as taking a time of 150 seconds or more. When we add this to the table, we
have a descending cumulative frequency of zero.
We now need to plot these values as
coordinates on a grid. The 𝑥-axis will represent the time
in seconds, and the 𝑦-axis will represent the descending cumulative frequency. Each set of values will have the
lower boundary of each class as the 𝑥-coordinate and the corresponding descending
cumulative frequency as the 𝑦-coordinate. We therefore need to plot the six
points zero, 100; 30, 97; 60, 80; 90, 45; 120, two; and 150, zero. This corresponds to the cumulative
frequency diagram in option (C).
Whilst options (A) and (B) look
similar, they have incorrect coordinates at 120, zero and 30, 100, respectively. We can therefore conclude that the
correct descending cumulative frequency diagram is option (C).
