Video Transcript
The table shows the number of
hours that 100 students spent revising for an exam. Determine the missing
cumulative frequency results.
The grouped frequency table
presents the data on the number of hours that students spent studying. The groups or classes have open
intervals such that the first group, zero dash, represents values of zero hours
or greater but less than two. This is because the next group
begins with values greater than or equal to two. We do not have overlapping
values in a grouped frequency table.
We are asked to complete the
cumulative frequency table based on the frequencies. The cumulative frequency gives
the running total of the frequencies. An ascending cumulative
frequency will always represent the frequencies of values that are less than a
particular value. The first group in the
frequency table has a cumulative frequency of zero. This is because we can conclude
from the frequency table that there were zero students revising for less than
two hours. To find the second cumulative
frequency value, we add the frequency of the second group to the previous
cumulative frequency. There are 10 students who
revised for less than four hours. Hence, the second cumulative
frequency is 10 plus zero, which equals 10.
We now need to determine the
cumulative frequency of students who revised for less than six hours. The class four dash in the
grouped frequency table indicates that 19 students revised four hours or more
and less than six hours. However, the 10 students in the
previous group also revised for less than six hours. Hence, the cumulative frequency
for less than six hours is equal to 19 plus 10, which equals 29. This third cumulative frequency
was found by adding the frequency of the third class to the previous cumulative
frequency.
We can then continue this
process to find each of the cumulative frequency values. It is worth noting that the
cumulative frequency of all values will be the same as the total frequency. This is useful for checking
whether our values are correct. The total frequencies can be
calculated as zero plus 10 plus 19 plus 37 plus 24 plus 10, which equals
100. Since the final cumulative
frequency is also 100, then we have confirmed that the missing cumulative
frequency values are zero, 10, 29, 66, 90, and 100.
