### Video Transcript

A manufacturer samples the
mass, in grams, of 30 pencils from their production line. Their masses are recorded in
the table. No pencil has a mass greater
than 60 grams. Which cumulative frequency
graph correctly shows this information? Is it graph (A), (B), (C), (D),
or (E)?

In order to identify the
correct graph, we need to calculate the cumulative frequencies for the values in
the table. This will give us a running
total for values that are less than a given point. The less than value that we
will use will be the upper boundary of each class.

We begin by recognizing that
the first group in the table represents masses that are 10 grams or greater but
less than 20 grams. We can add the cumulative
frequency row to our table, which will represent pencils with a mass of less
than 20 grams, less than 30 grams, less than 40 grams, and so on. Since no pencil has a mass
greater than 60 grams, the last element of the cumulative frequency row
represents the number of pencils with masses less than 60 grams.

Recalling that cumulative
frequency is the running total, we have values of three, nine, 20, 27, and
30. Note that we calculate these
values by adding the frequency in that column to the previous cumulative
frequency value. The final cumulative frequency
will be the same as the total frequency. In this case, this will be the
value 30, since 30 pencils were sampled.

When drawing or identifying the
cumulative frequency graph in this context, we have the mass on the 𝑥-axis and
cumulative frequency on the 𝑦-axis. The 𝑥-coordinate values will
be the less than mass values or the upper boundaries of each class. This allows us to use a
cumulative frequency curve to identify values that are less than any particular
value. The coordinates that would be
plotted can be given as 10, zero; 20, three; 30, nine; 40, 20; 50, 27; and 60,
30. As previously stated, the
𝑥-coordinate is the upper boundary of each group and the 𝑦-coordinate is the
corresponding cumulative frequency. The graph that matches these
coordinates is that of graph (B). And so this is the cumulative
frequency graph for the given information.