# Question Video: Identifying the Correct Descending Cumulative Frequency Graph Mathematics

The following table shows the heights of players in a basketball game. Note that no player is taller than 200 cm. Which of the following is the descending cumulative frequency graph? [A] Graph A [B] Graph B [C] Graph C [D] Graph D [E] Graph E

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### Video Transcript

The following table shows the heights of players in a basketball game. Note that no player is taller than 200 centimeters. Which of the following is the descending cumulative frequency graph? Is it graph (A), (B), (C), (D), or (E)?

The descending cumulative frequency of a value 𝑥 indicates the frequency of values that are greater than or equal to 𝑥. In order to identify which descending cumulative frequency graph represents the given data, we can first calculate these values. We note that the first group in the frequency table is that of 140 dash, indicating a height of 140 centimeters or greater, up to but not including 150 centimeters, since this is the lower boundary of the next group. Therefore, the first descending cumulative frequency will be for heights that are 140 centimeters or greater.

We see from the table that there were a total of 30 players. And as all 30 have a height of 140 centimeters or greater, the first descending cumulative frequency is 30. Next, we consider how many players had a height of 150 centimeters or greater. This will be the total of 30 players minus those players from the first group, those with a height greater than or equal to 140 centimeters, but less than 150 centimeters. 30 minus four equals 26. So, our second descending cumulative frequency is 26.

We then repeat this process by subtracting six from 26. The third descending cumulative frequency, which represents those players with a height greater than or equal to 160 centimeters, is therefore equal to 20. Continuing this process, we have three further descending cumulative frequency values of 11, eight, and one.

At this stage, we note that we typically finish a descending cumulative frequency with a value of zero. To do this, we consider the last class to have the same class width as the others and define an additional class in the distribution. In this question, this would be 200 dash, which corresponds to those players with a height of 200 centimeters or greater. This group has a descending cumulative frequency value of zero.

To draw the descending cumulative frequency graph, we plot the height on the 𝑥-axis and the descending cumulative frequency on the 𝑦-axis. The coordinates are given by lower boundary of each class, descending cumulative frequency. Hence, the first coordinate is 140, 30. Next, we have 150, 26, followed by 160, 20; 170, 11; 180, eight; 190, one; and 200, zero.

Inspecting the given answer options, we can observe that the given graph in option (C) is the correct descending cumulative frequency graph. Whilst options (B) and (E) are very similar, we note that they have incorrect coordinates at 150, 30 and 200, one, respectively.

We can therefore conclude that the correct answer is option (C).