A-Level Maths: L1-07 [Data: Median and Quartiles from Histograms]

[@satwikasaran7757]

I have a few questions! How can you be sure that the median is 8? For example if there a 20 data points in the 6 to 8 interval, isn’t it possible that all the 20 of them are 7? Furthermore, going by what you said... In that class interval, x is greater than or equal to 6 but less than 8, so how can the median be 8, as the 25th value must still be in that interval, but you can never be sure what number it is (as it’s grouped)? Sorry... I am a little confused, please reply!

[@harrysmith2184]

I have the same question

[@fishhvm8hi33]

you assume that all the values are evenly spread in the range (even tho thats probably isnt true)

[@shaheerziya2631]

Since there is uncertainty about the exact value in that interval, (i.e. it could be 6, 6.9 , 6.69420 ,7) it’d be inaccurate to say that the media is 8. However we are certain that the median is in fact in this interval. This assumes that the data is uniformly distributed.

[@muhammadwaleed124]

i think you can use interpolation to be sure?

[@Just_Shaun]

Yeah, interpolation would get you an exact value for the median. Though it is 8 because If you use interpolation, the actual median would be 6 + (20/20 * 2 ) which is 8. *Edit, though obviously in a real situation, the data wouldn’t be completely uniformly distributed. But for alevel maths we assume it is uniform which makes it way easier.

[@krishmakkar7249]

Hello, just a question, why can you not start your interpolation from the second class width in order to find the LQ? Doing ((2/10)*7.5)+6.

[@TLMaths]

I did use the 2nd class width? Your calculation isn't quite right though as there are 20 bits of data in the 2nd interval, so you should have ((2/20)*7.5)+6

[@girlonline3742]

For interpolation in the “Pearson edexcel statistics and mechanics year 1/as” they say to use 5.5 and 9.5 for an interval of E.g 5-9 instead of 5 and 9 could you explain this I’m so confused

[@TLMaths]

If you had intervals that said 1-4 5-9 10-14 etc Then for the 5-9 grouping, this would represent 4.5 ≤ x < 9.5 (if the data doesn't represent age). So 4.5 and 9.5 would be the endpoints. Not sure what it means if it's using 5.5 and 9.5. I'd need to see the textbook (unfortunately I don't own it - I don't teach Edexcel)

[@privatecaller7209]

Hello Sir, How do you determine the values to use when interpolating? For grouped continuous data, I would've thought that, for example, the group 6

[@TLMaths]

5.5 would go in the 5≤x

[@katt5932]

How can the median be 8 when we know that it is in the group since in that group x is les than 8 and greater than 6 so if it was 8 that would be the next group down?

[@TLMaths]

The median is just an estimated value. There are 25 bits of data in the first two groups, and 25 bits of data in the second two groups. So 8 is bang in the middle.

[@createa817]

Hello, how do you find the mean of a histogram?

[@TLMaths]

It's the same way you find the mean from grouped data, using the midpoint of the class interval as x.

[@createa817]

@@TLMaths So I am given a histogram and I need to find the mean. The midpoint of each "bar" * its frequency, then divide by the total frequency?

[@TLMaths]

Yep

[@nano7yt617]

Sir do we need to know this for aqa ??

[@TLMaths]

You don't need to do linear interpolation, estimating median from grouped data, for AQA.

[@johnsergie3906]

At 1:50 how did you know it was 12.5

[@TLMaths]

50/4=12.5

[@ctds]

Nice

[@harrysmith2184]

Can the constant k in a proportion ever be negative?

[@TLMaths]

It wouldn't really make a whole lot of sense for it to be negative. It'd be like drawing the bars downwards.

[@harrysmith2184]

@@TLMaths Does this apply to proportion in general? If two variables are proportional can the constant be negative? Sorry for being unclear.

[@TLMaths]

This explains it better: www.wyzant.com/resources/answers/79013/why_do_proportional_relationships_have_to_have_a_positive_slope

[@bob_swims3324]

Hero

[@bkayzl]

i dont get the UQ at all

[@JK-vm7yo]

Ur allowed to use calculators to work this all out dw

[@freerights6695]

@@JK-vm7yo howd u do that?

[@tomtricks6838]

if i pass ima send you 100