### Video Transcript

The table represents the time taken
by some people to travel to work. Calculate an estimation for the
modal number of minutes the people take to travel to work.

The table that we are given showing
the time taken for people to travel to work is in the form of a grouped frequency
table. For example, 10 people take a time
of 4.5 minutes or more up to but not including 9.5 minutes to get to work. We are asked to calculate an
estimate for the mode, and the mode is the most common value or values. It’s not possible to extract the
mode from a grouped data set. The only thing we can do from a
grouped frequency table is recognize the modal class, which is the class with the
highest frequency. As the class 9.5 minutes or more
has the highest frequency of 15, then this is the modal class.

So, from the table, we have
identified the modal class, and we can further identify an estimate for the mode by
drawing a histogram. There are some important points to
note when drawing a histogram. When we have a histogram, we don’t
have bars with spaces in between them. Instead, we have a continuous
𝑥-axis representing the variable, which will be time in minutes here. The rectangular bars representing
the frequencies have their vertical line segments on the upper and lower boundaries
of each class.

So, once we have our histogram, we
identify the modal class, which is the class with the highest bar. We then draw two lines from each of
the top corners of this modal class bar to the adjacent corners of the classes on
each side, which will look something like this. We then draw a vertical line from
the point of intersection to the 𝑥-axis. We can use the grid lines to help
us identify this estimate for the mode. Therefore, we can give the answer
that an estimate for the modal number of minutes the people took to travel to work
is 11.5 minutes.