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Mean, Median and Arithmetic Progression (AP)

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Vijay1998
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Mean, Median and Arithmetic Progression (AP) [#permalink] New post   16 Jul 2021, 23:03
We all know that if a sequence is in AP then Mean = Median.
My doubt is its opposite is also true?
That is, if in a pattern/sequence Mean = Median then that pattern/sequence is in AP?
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bansalgaurav
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Re: Mean, Median and Arithmetic Progression (AP) [#permalink] New post   16 Jul 2021, 23:21
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Vijay1998 wrote:
We all know that if a sequence is in AP then Mean = Median.
My doubt is its opposite is also true?
That is, if in a pattern/sequence Mean = Median then that pattern/sequence is in AP?


No the opposite is not true. check the case::
S = {5 , 15,15, 25}. Mean = Median =15.
The data points in this set are not in AP as the difference between 2nd and 3rd data points is not equal to the difference between the other two consecutive numbers.
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ramlala
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Re: Mean, Median and Arithmetic Progression (AP) [#permalink] New post   17 Jul 2021, 19:41
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Vijay1998 wrote:
We all know that if a sequence is in AP then Mean = Median.
My doubt is its opposite is also true?
That is, if in a pattern/sequence Mean = Median then that pattern/sequence is in AP?


Hi Vijay1998

We can not say that if in a pattern/sequence Mean = Median than that pattern/sequence is in AP
bansalgaurav has explained directly with example
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Vijay1998
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Re: Mean, Median and Arithmetic Progression (AP) [#permalink] New post   17 Jul 2021, 22:16
bansalgaurav wrote:
Vijay1998 wrote:
We all know that if a sequence is in AP then Mean = Median.
My doubt is its opposite is also true?
That is, if in a pattern/sequence Mean = Median then that pattern/sequence is in AP?


No the opposite is not true. check the case::
S = {5 , 15,15, 25}. Mean = Median =15.
The data points in this set are not in AP as the difference between 2nd and 3rd data points is not equal to the difference between the other two consecutive numbers.


Thanks for the explanation Gaurav Bansal. Really appreciate it.
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bansalgaurav
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Re: Mean, Median and Arithmetic Progression (AP) [#permalink] New post   18 Jul 2021, 02:00
Vijay1998 wrote:
bansalgaurav wrote:
Vijay1998 wrote:
We all know that if a sequence is in AP then Mean = Median.
My doubt is its opposite is also true?
That is, if in a pattern/sequence Mean = Median then that pattern/sequence is in AP?


No the opposite is not true. check the case::
S = {5 , 15,15, 25}. Mean = Median =15.
The data points in this set are not in AP as the difference between 2nd and 3rd data points is not equal to the difference between the other two consecutive numbers.


Thanks for the explanation Gaurav Bansal. Really appreciate it.


You're welcome mate ... keep sharing more questions :thumbsup: :thumbsup: !!!
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Re: Mean, Median and Arithmetic Progression (AP) [#permalink]
18 Jul 2021, 02:00
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