Video: Pack 1 • Paper 3 • Question 3

Pack 1 • Paper 3 • Question 3


Video Transcript

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 38.

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 intervals.

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.

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