for which of the frequency distributions is the mean equal

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If the variables P ,Q and R can be equal only to integers between 1 and 7 inclusive, with frequencies indicated by the shaded regions above, for which of the frequency distributions is the mean equal to the median?

(A) P only
(B) Q only
(C) R only
(D) P and Q
(E) Q and R
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Q.png
R.png
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by kunal_kc » Sat Jan 30, 2010 3:52 am
I did it by the basic method by finding the mean and median for each..

First take the mean for all by = sum of numbers / number of terms, so mean for

R= 86/20
Q= 84/21= 4
P= 68/17=4

then find the median (middle number or average of middle numbers if number of terms is odd)

which for P & Q is also 4

hence P & Q have the same mean and median. answer D

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by sanju09 » Sat Jan 30, 2010 4:11 am
bhumika.k.shah wrote:If the variables P ,Q and R can be equal only to integers between 1 and 7 inclusive, with frequencies indicated by the shaded regions above, for which of the frequency distributions is the mean equal to the median?

(A) P only
(B) Q only
(C) R only
(D) P and Q
(E) Q and R
Looking for some added technology as it seems like the concept of finding median in particular, using cumulative frequency table may be a useful idea here. Please wait!!
Last edited by sanju09 on Sat Jan 30, 2010 4:18 am, edited 1 time in total.
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by bhumika.k.shah » Sat Jan 30, 2010 4:13 am
sowree :-(
the OA is D
P and Q


Could u explain how u took for each diagram 1,1,2 .... ???

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by sanju09 » Sat Jan 30, 2010 4:20 am
bhumika.k.shah wrote:sowree :-(
the OA is D
P and Q


Could u explain how u took for each diagram 1,1,2 .... ???
Thanks for not quoting me, just wait if you please!!
The mind is everything. What you think you become. -Lord Buddha



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by bhumika.k.shah » Sat Jan 30, 2010 4:22 am
did u score a 760 or is that ur targetted score?
sanju09 wrote:
bhumika.k.shah wrote:sowree :-(
the OA is D
P and Q


Could u explain how u took for each diagram 1,1,2 .... ???
Thanks for not quoting me, just wait if you please!!

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by sanju09 » Sat Jan 30, 2010 4:46 am
bhumika.k.shah wrote:did u score a 760 or is that ur targetted score?
sanju09 wrote:
bhumika.k.shah wrote:sowree :-(
the OA is D
P and Q


Could u explain how u took for each diagram 1,1,2 .... ???
Thanks for not quoting me, just wait if you please!!
just wait bhoomi, and have faith in what's displayed
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by bhumika.k.shah » Sat Jan 30, 2010 8:02 pm
OMG! thanks for taking sooo much effort to explain it to me :-)

I started solving the sum tht way but then lost patience! :-(

Thanks! :D
sanju09 wrote:
bhumika.k.shah wrote:did u score a 760 or is that ur targetted score?
sanju09 wrote:
bhumika.k.shah wrote:sowree :-(
the OA is D
P and Q


Could u explain how u took for each diagram 1,1,2 .... ???
Thanks for not quoting me, just wait if you please!!
just wait bhoomi, and have faith in what's displayed

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by bhumika.k.shah » Sat Jan 30, 2010 8:03 pm
Just one question!!

how wud it strike to u that u have to take the cumulative frequencY???
sanju09 wrote:
bhumika.k.shah wrote:did u score a 760 or is that ur targetted score?
sanju09 wrote:
bhumika.k.shah wrote:sowree :-(
the OA is D
P and Q


Could u explain how u took for each diagram 1,1,2 .... ???
Thanks for not quoting me, just wait if you please!!
just wait bhoomi, and have faith in what's displayed

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by kunal_kc » Sat Jan 30, 2010 11:17 pm
great, i think you got your explanation. good work sanju.


cheers!

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by sunil_snath » Sun Jan 31, 2010 12:23 am
Quick Question on this tho,

If this problem shows up in the GMAT, wouldnt finding the mean and median of the figure take a long time?

My method was to quickly deduce the answer from the figures. Since Figure R is complex I left it alone.

P&Q are symmetrical. If you look at it, the frequencies of 1's and 7's, 2's and 6's, 3's and 5's are the same in these figures which always brings the total mean to 4. And this same logic brings us to a conclusion that 4 is the middle value.

Now since the answer choices only list 1 or 2 out of P, Q and R. The answer is D - P & Q.

Is there something I might have missed in the logic?

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by sanju09 » Sun Jan 31, 2010 11:05 pm
bhumika.k.shah wrote:
Just one question!!

how wud it strike to u that u have to take the cumulative frequencY???
Alright, Miss QB! I also enjoy replaying my school days and talking about basics. In Statistics Mean, Median and Mode are known as the measures of central tendencies. Median is the middle most value of the observations when the observations are either arranged in increasing or decreasing order.

Preparing a cumulative frequency distribution table is the first step in calculating the median of the grouped data. The cumulative frequency of a class is obtained by adding the frequencies of all the classes preceding the given class. To calculate the median either the more than or less than cumulative frequency is used.

If the data is converted into a frequency distribution table it is known as grouped data. The median for the grouped data is given by l + [{(n/2) - c f}/f]*h.

Where l is lower class limit of median class,

n is total number of observations

c f is the cumulative frequency of the class preceding the median class, and

f is the frequency of the median class and h is the class size.

But, in this question, we don't have the class intervals to group the data. We straight away have the terms as an alternative to make business far easier. After preparing a cumulative frequency distribution table, in the present case, all we need to look for is which item(s) in order is median, and where would it actually lie. Practicing one or two questions of each kind of distribution would enable any normal aspirant catch the required efficiency on test.

sunil_snath wrote:

Is there something I might have missed in the logic?
Hi sunil, your approach is amazing! Totally appropriate thought under difficult test conditions! I call such events, awe-inspiring!!
The mind is everything. What you think you become. -Lord Buddha



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by bhumika.k.shah » Mon Feb 01, 2010 3:28 am
sanju09 wrote:
Alright, Miss QB!

???????????????????????

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by sanju09 » Mon Feb 01, 2010 4:07 am
bhumika.k.shah wrote:
sanju09 wrote:
Alright, Miss QB!

???????????????????????
guess what
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by bhumika.k.shah » Mon Feb 01, 2010 4:15 am
sanju09 wrote:
bhumika.k.shah wrote:
sanju09 wrote:
Alright, Miss QB!

???????????????????????
guess what
??????????????????????????????????????????????????????????