Video Transcript
An employer surveyed 30
employees to determine the distance in kilometers of their commute to work. The data is given in the
descending cumulative frequency graph. Determine an estimate for the
median commuting distance.
In this question, we are given
a descending cumulative frequency graph. The descending cumulative
frequency is different to ascending cumulative frequency because we say that the
descending cumulative frequency of a value 𝑏 is the frequency of values that
are greater than or equal to 𝑏. In an ascending cumulative
frequency graph, the values are the less than values. So for example, the coordinate
10, 24 indicates that 24 employees had a commuting distance that was greater
than or equal to 10 kilometers.
Now given that we have this
descending cumulative frequency, we are asked to find an estimate for the
median. And we can recall that the
median is the middle value when the data is in ascending or descending
order. And we are asked for an
estimate for the median because we have a grouped data set. So that means we can’t find the
exact median. It doesn’t mean that we should
try to guess what it is.
To find the position of the
median, we calculate the total frequency divided by two. The total frequency in this
problem is the total number of employees. We were told that there were 30
employees surveyed, but even if we weren’t given this information, we could
determine it from the graph. The highest value in the
descending cumulative frequency is the first value, since 30 employees had a
commuting distance greater than or equal to zero kilometers. The median position is
therefore 30 over two, which is 15. If we lined up all the
employees from the smallest distance commuted to the largest distance commuted,
the median distance commuted would belong to the 15th person.
So how do we know what distance
they traveled? Well we can use the graph. We draw a horizontal line at
the median position, that’s 15, on the descending cumulative frequency until it
meets the curve. Then we draw a vertical line
downwards to the 𝑥-axis, which gives us 19. Therefore, we can give the
answer that an estimate for the median distance commuted is 19 kilometers.
