### Video Transcript

The grouped frequency table gives
information about the weight of 40 monkeys in a zoo. Part a) What is the modal class
interval for the data in the table? Part b) The graph shows an
incorrect frequency polygon drawn for the information in the table. Identify two things wrong with the
frequency polygon.

The mode means the most common. In this case, to find the modal
class, we need the class with the highest frequency. There were 30 monkeys that were
greater than 25 kilograms, but less than or equal to 30 kilograms. 26 monkeys were between 30 and 35
kilograms, 23 between 35 and 40, 11 between 40 and 45 kilograms, nine between 45 and
50, and four between 50 and 55 kilograms. The highest frequency is 26. Therefore, the modal class interval
is between 30 and 35 kilograms. 𝑤 is greater than 30, but less
than or equal to 35.

The second part of our question
asked us to identify two things wrong with the frequency polygon. When drawing any frequency polygon
for grouped data, our first step is to find the midpoint of each group, in this case
27.5 kilograms, 32.5, 37.5, and so on. We then plot these points on the
diagram, as shown in pink. We go along to 27.5 kilograms and
up to a frequency of 13. We then repeat this process for the
other five points, along to 32.5 and up to 26, along to 37.5 kilograms and up to a
frequency of 23, and so on for the other three points. This means that the first thing
that is wrong with our frequency polygon is that the points should be plotted in the
middle of the weight interval.

We were asked to find two things
wrong, so what else is wrong with the frequency polygon? Well, the second thing that is
wrong is that the frequency polygon should not be a closed shape. The line that joins the first and
the last point should not be on the graph. We have, therefore, identified two
different things that are wrong with the frequency polygon.