Video Transcript
A statistician collected data on
the masses of a population of birds. She then produced a box plot and a
histogram of the masses. From which graph can the exact
value of the median be identified? From which graph could you
calculate the total population of birds? From which graph could you
calculate the exact value of the interquartile range?
We recall that a box plot or
box-and-whisker plot can be drawn as shown. It is drawn to show the range of
values as well as the median, quartiles, and interquartile range. The minimum and maximum values are
the ends of the whiskers. In this case, this will be the
lowest and highest mass of the population of birds. The ends of the box identify the
lower quartile and upper quartile, and the line inside the box represents the
median.
The interquartile range is equal to
the upper quartile minus the lower quartile. This means that we can also
calculate this easily from a box plot. This means that the correct answer
for the first and third parts of this question is the box plot, as the median and
interquartile range can be identified and calculated from the box plot.
A histogram is used to show
frequency and compare items. Each bar represents an interval of
values. In some locations, the 𝑦-axis is
represented by the frequency density instead of the frequency. Either way, we can calculate the
total population by adding all the frequencies. The correct answer for the second
part of this question is the histogram.
