# Cumulative frequency diagram

##### New member
Hit a wall on this, older student ( very old ?)
how would you approach this question please before I give up! I’m sure it’s easy but I’m overthinking it as usual.
thank you

On a cumulative frequency diagram, the median time is found by going halfway up the cumulative frequency (vertical axis), in this case up to 40 (ie a half of 80) and reading off the corresponding time. On the red curve this gives a median of 25. Can you see that?

The quartiles are found by going a quarter (and then three quarters) of the way up the vertical axis and reading off the corresponding times.

Let us know what you get.

What information is each graph giving you? For example, the red graph passes though the point (15,20). What is the meaning of this point?

On a cumulative frequency diagram, the median time is found by going halfway up the cumulative frequency (vertical axis), in this case up to 40 (ie a half of 80) and reading off the corresponding time. On the red curve this gives a median of 25. Can you see that?

The quartiles are found by going a quarter (and then three quarters) of the way up the vertical axis and reading off the corresponding times.

Let us know what you get.
Hi
yes I can see that the red line median is 25 and the blue line is 32 which would suggest at this point that the red line the fastest at completing the task
however the LQ for the red line is 15 and the UQ is 35 = IQR of 20
the UQ for the blue line is 27 and the UQ is 35 = IQR of 8
but what does this actually tell me ?

What information is each graph giving you? For example, the red graph passes though the point (15,20). What is the meaning of this point?
Hi,
good question. The point 15,20 tells me that 20 pupils completed the task in 15 minutes
but I’m not sure how to proceed from here to see the overall result ?
ie who was the slowest at completing the task
thank you so much

Hi,
good question. The point 15,20 tells me that 20 pupils completed the task in 15 minutes
but I’m not sure how to proceed from here to see the overall result ?
ie who was the slowest at completing the task
thank you so much
Actually, the point (15,20) tells you that 20 pupils completed the task in 15 minutes OR LESS.

As you have stated in post #4:
The median time for Red is 25 minutes ie 50% of pupils finished in 25 min or less.
The median time for Blue is 32 minutes, ie 50% of pupils finished in 32 min or less.

The LQ and UQ for Red are 15 and 35 respectively, ie the middle 50% of pupils took between 15 and 35 min.
The LQ and UQ for Blue are 27 and 35 respectively, ie the middle 50% of pupils took between 27 and 35 min.

So, using these figures and their meanings, which group, on average, was slowest at completing the task?

Based on the findings I would say the blue team were the slowest.
if the question asks for the average though, why couldn’t I just use the median ?
im struggling a bit with the relevance if LQ and UQ ( sorry ?)
( I should have stuck to knitting )

If you relied on only the median, you could conclude that, on average, the blue team were the slowest.

I have drawn the box-and-whisker plots for the two sets of data. I hope you are familiar with these sorts of plots - they basically illustrate the 5- number summary for a set of data ie, lowest, LQ, median, UQ, highest, breaking the data in quarters.

If you compare the "whiskers" at the right-hand end, you can see that the slowest 25% of students in the red team took between 35 and 50 min to finish the test. The slowest 25% of students in the blue team took between 35 and 40 min.

This complicates things a bit. Can you still conclude that, on average, the blue team are slowest?

I think "yes" when you compare medians only and because the question says "on average. But the box-plot based on the quartiles add another dimension to the question. I think there are valid arguments either way.

Also compare at the fastest 25% in each group. The fastest in red finished in under 15 min, while the fastest in blue finished in 27 min. What conclusion does that support?