The table shows how long 60 people
spent waiting for a train last Monday. Part a) In which class interval
does the median lie? Part b) Draw a frequency polygon to
represent the data.
So looking at part a, in which
class interval does the median lie? So first, well, we need to remind
ourselves what the median is. And it’s actually the middle value
if our numbers are actually in numerical order. And in our table, the values are
actually in numerical order. So all we need to do is actually
find out in which one of our class intervals the middle number will lie. To find the median value, what we
actually do is use this formula. And that’s 𝑛 plus one divided by
two, where 𝑛 is our total frequency.
Okay, so let’s use that to find out
where our median value is going to lie. So we know that the table shows the
data for 60 people. So therefore, our 𝑛 value is gonna
be equal to 60. So therefore, the 60 plus one over
twoth value is gonna be our median value. So it’s gonna give us 61 over
two. So if we divide 61 by two, we get
30.5. So therefore, what we can say is
that our median value is gonna be between the 30th and 31st values.
Now to actually help us find out
where the 30th and 31st values are gonna be, I’m actually gonna work out the
cumulative frequency. So we’re gonna start with 17. And then our next value for the
cumulative frequency is gonna be 38. And therefore, we know actually we
don’t have to go any further because our 30th and 31st values are actually gonna be
within this interval because it’s greater than 17, but they’re both less than
So therefore, we can say that the
median lies in the interval 𝑡 is greater than 10 but less than or equal to 20. Okay, great! So we’ve solved part a. Let’s move on to part b.
And in part b, we need to draw a
frequency polygon to represent the data. The key thing to remember when
we’re doing this is actually if we’re gonna draw a frequency polygon to represent
the data, we need to remember to use the midpoints, so the midpoints of our
So in order to actually find the
midpoints for each of our intervals, what we do is we actually add the two values in
our interval together and then divide by two, cause that finds the middle point. So therefore, our first midpoint is
gonna be five because zero plus 10 is 10. Divide that by two, we get
five. And if we use the same method for
the next intervals, we’re gonna get midpoints of 15, 25, 35, and 45.
Okay, great! So now we’ve got our midpoints. We can actually start to draw our
frequency polygon. So if we look at our frequency
polygon, we can see that we’ve got frequency as our 𝑦-axis and time waiting in
minutes as our 𝑥-axis. So what this is gonna be is
frequency is gonna be our 𝑦-value and the midpoint is gonna be our 𝑥-value.
So here we’ve actually plotted our
first point at five, 17. And it’s here that we make sure
that our scale we actually know. So in this case, the scale’s gonna
be one little square equals one. So that’s both in frequency and
time waiting. Then our next point is at 15, 21;
25, 15; then the next one at 35, five; and then finally 45, two.
Okay, great! So what we’ve done now is we
actually plotted all of our points. So the final thing we need to do to
finish our drawing of a frequency polygon is actually join these with straight
lines. So there we have it. We’ve got a completed frequency
diagram which represents our data.