Video Transcript
For the given histogram, which of
the following is the best estimate of the mode? Option (A) 12, option (B) 40,
option (C) 50, option (D) 30, or option (E) 44.
We can recall that the modal class
of a grouped frequency distribution is the class or classes with the highest
frequency. When we are using a histogram with
classes of equal width, the class with the highest frequency is the class with the
highest bar in the histogram. We can therefore identify that the
modal class here is that of the class 40 dash. The values in this class will be 40
or greater but less than 50, which is the boundary of the next class.
But of course, in this question, we
need to find an estimate for the mode rather than simply the modal class. We can understand that the mode
will lie within the modal class, which will be values from 40 up to but not
including 50. The estimates in option (A) and (D)
can therefore not be correct. To find an estimate for the mode
using the histogram, we can apply the steps we need to take to estimate the mode
graphically.
Once we have identified the modal
class, we draw a straight line connecting the top-left corner of this tallest bar to
the top-left corner of the rectangle representing the frequency of the following
class. Next, we draw a straight line
connecting the top-right corner of the tallest bar to the top-right corner of the
rectangle representing the frequency of the class immediately before. Then, from the point of
intersection of these lines, we draw a vertical line down to the 𝑥-axis. This point on the 𝑥-axis
represents an estimate for the mode. We can see that this line lies
slightly to the left of the midpoint of 40 and 50. Therefore, we can give the answer
that an estimate for the mode must be the value of 44.
