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Median of grouped data!

Im doing the AQA S1 test. Median of grouped data is really annoying me.

I have a TI-83 which calculates median, but when entering data I can only enter in midpoints as x values.

Does anyone know how to enter in groups e.g. 10-12 instead of midpoint- 11.

Much appreciate any help!
Reply 1
Avatar for Robob
Robob
17
why do you need a calculator?
Reply 2
Avatar for samd
samd
10
Biffy Clyro
Im doing the AQA S1 test. Median of grouped data is really annoying me.

I have a TI-83 which calculates median, but when entering data I can only enter in midpoints as x values.

Does anyone know how to enter in groups e.g. 10-12 instead of midpoint- 11.

Much appreciate any help!


Erm for grouped gata you have to use the midpoints to find the median. It isn't too difficult to work out the midpoints yourself is it? And then plug them in.

Even better do it without a grphical calculator through the standard interpolation method.
Reply 3
Avatar for Biffy Clyro
Biffy Clyro
OP
12
The examples in my book are rubbish.

Ok, try this question:

Time to complete a puzzle___ Frequency
20-39_____________________6
40-49_____________________8
50-54_____________________7
55-59_____________________ 5
60-99_____________________ 9
100+ _____________________ 5

Total: 40

Find the estimate of the median.

Cheers

--------------

I know you can use the midpoints, but that does not give the exact estimate of the median.

For instance, the question above using midpoints gives 52. That is not the answer.
Reply 4
Avatar for Robob
Robob
17
Biffy Clyro
The examples in my book are rubbish.

Ok, try this question:

Time to complete a puzzle___ Frequency
20-39_____________________6
40-49_____________________8
50-54_____________________7
55-59_____________________ 5
60-99_____________________ 9
100+ _____________________ 5

Total: 40

Find the estimate of the median.

Cheers

--------------

I know you can use the midpoints, but that does not give the exact estimate of the median.

For instance, the question above using midpoints gives 52. That is not the answer.


That's because you've worked it out wrong....

I got 54.1, it might be wrong if ive made a mistake
Reply 5
Avatar for Biffy Clyro
Biffy Clyro
OP
12
hmmm.. well that isnt the right answer either apparently.

I can be sure that upon entering the right details: Midpoints are: 29.5, 44.5, 52, 57, 79.5, anything above 100. I get 52.0 as the median.. but its wrong.

Very confused :frown:
Reply 6
Avatar for Excalibur
Excalibur
15
rpotter
That's because you've worked it out wrong....

I got 54.1, it might be wrong if ive made a mistake


I got 54.1 as well...
I get 53.78, probably because the above two are using 0.5(n+1) rather than just 0.5n, although my stats book says you should use 0.5n for the median of grouped data. If your answer book disagrees, it's probably wrong.
Reply 8
Avatar for Biffy Clyro
Biffy Clyro
OP
12
53.78 is correct!

I cant seem to get that value though! If you could summarise your working quickly for me I would be extremely grateful.

I really don't know how I keep getting it wrong, Im supposed to be good at Maths :rolleyes:
Look up interpolation in grouped data. Basically, the formula is:

median = b + ((1/2*n - f)/f[c]) * c

where b = the lower class boundary of the median class, f is the sum of the frequencies below b, f[c] is the frequency of the actual median class, and c is the width of the median class (n is the total frequency).

so in this case,

median = 49.5 + ((20-14)/7)*5 = 53.78
Reply 10
Avatar for Biffy Clyro
Biffy Clyro
OP
12
Thank You sooooo much!

That is perfect..! My stupid book's explanation was very poor.
Reply 11
Avatar for Robob
Robob
17
skidjzu
Look up interpolation in grouped data. Basically, the formula is:

median = b + ((1/2*n - f)/f[c]) * c

where b = the lower class boundary of the median class, f is the sum of the frequencies below b, f[c] is the frequency of the actual median class, and c is the width of the median class (n is the total frequency).

so in this case,

median = 49.5 + ((20-14)/7)*5 = 53.78


hmm, never seen that before, when I did S1 always did it a different way and got it correct, might be different boards i spose
Pls, just so I'm sure. Are you saying the use of 0.5(n+1) is wrong for calculating grouped data median by interpolation formula as against 0.5n?????
Original post by darthsidious
Look up interpolation in grouped data. Basically, the formula is:

median = b + ((1/2*n - f)/f[c]) * c

where b = the lower class boundary of the median class, f is the sum of the frequencies below b, f[c] is the frequency of the actual median class, and c is the width of the median class (n is the total frequency).

so in this case,

median = 49.5 + ((20-14)/7)*5 = 53.78


Pls, just so I'm sure. Are you saying the use of 0.5(n+1) is wrong for calculating grouped data median by interpolation formula as against 0.5n?????
Original post by Compbrains
Pls, just so I'm sure. Are you saying the use of 0.5(n+1) is wrong for calculating grouped data median by interpolation formula as against 0.5n?????


There are various different conventions. Go with whatever your syllabus/textbook suggests.

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