Video Transcript
Complete the following descending
cumulative frequency table. Note that no player is taller than
200 centimeters.
Let’s start this question by
looking at the data represented. Here, we are considering the
heights of different players. For example, these could be
basketball players or soccer players. The row for number of players
represents the frequencies for each group of heights.
Looking at the first height
grouping, this is 140 dash. In this group will be the heights
which are 140 centimeters or more, up to but not including 150 centimeters. We say that the first group would
have an upper boundary of 150 centimeters, because that’s the lower boundary of the
following class.
The final row in the table is CF,
which stands for cumulative frequency. But we need to be very careful here
because this is a descending cumulative frequency. We can recall that the descending
cumulative frequency of a value 𝑥 indicates the frequency of values that are
greater than or equal to 𝑥. If we have an ascending cumulative
frequency, then these cumulative frequencies will increase as we go along, whereas
in a descending cumulative frequency, the cumulative frequencies will decrease to
zero.
So, the first value in the table
for the descending cumulative frequency will be the frequency or the number of
players who had a height greater than or equal to 140 centimeters. And that’s all the players. The first descending cumulative
frequency is always going to be the same as the total frequency, which in this case
is 30. And even if we weren’t given this
value of 30, we could also have worked it out by adding all the frequencies in the
row of the number of players.
Next, let’s see where the value of
26 comes from. Well, we are considering how many
players have heights which are greater than or equal to 150 centimeters. And that’s all the players
excluding the four players who we know had heights which are less than 150
centimeters. So we take the previous descending
cumulative frequency and subtract four, which is how the value of 26 was
obtained.
Now, let’s find the next four
missing descending cumulative frequencies. For the next cumulative frequency,
we need to find the frequency of heights which are greater than or equal to 160
centimeters. And we can think of this in two
ways, either that this is all the 30 players excluding those four plus six players
whose heights were less than 160 centimeters — that would give us 30 minus 10,
which is 20 — or we can use the same pattern as before, where we take the previous
frequency of six and subtract it from the previous descending cumulative frequency
of 26. That means that each time, the
descending cumulative frequency just changes by removing the frequency of the
previous group. And so 26 minus six is 20.
Next, we need to find the
descending cumulative frequency of heights which are 170 centimeters or more. So that’s the previous descending
cumulative frequency of 20 subtract the previous frequency of nine. And 20 take nine is 11. Then, we have the descending
cumulative frequency of heights greater than or equal to 180 centimeters. And 11 minus three is eight. For the final missing value for the
descending cumulative frequency, we calculate eight minus seven, which is one. And so we can list the missing
values from the table as 20, 11, eight, and one.
It is worth noting, however, that
usually we have descending cumulative frequencies such that they end with a
cumulative frequency of zero. And this is particularly true if we
are creating a graph of the values. In this context, a final descending
cumulative frequency of zero would represent the number of players who have heights
greater than or equal to 200 centimeters. And this zero is valid, because we
were also told in the question that no player is taller than 200 centimeters. However, the answer for the
question is simply the four missing values of 20, 11, eight, and one.
