0

I have following inputs

Sum of the squares of the numbers. For example if the numbers are $1,4,6$ the sum of squares is $53 = 1^2+4^2+6^2$.

And I have the number of input samples: $3$ in this case. Is it possible to calculate the standard deviation?

Note I don't have the actual numbers $1,4$ and $6$ just the sum of their squares that is $53$.

M47145
  • 4,106
Akshat Jiwan Sharma
  • 103
  • Can you construct two sets ${a_1, a_2, a_3}$ and ${b_1, b_2, b_3}$ for which $a_1^2 + a_2^2 + a_3^2 = b_1^2 + b_2^2 + b_3^2 = 53$ but the two sets have different standard deviations? Have you tried? If you did, it would immediately answer your question, and if you tried but failed, the failure might suggest how you could answer your question the other way. – MJD Oct 27 '14 at 17:53
  • Natural numbers? – barak manos Oct 27 '14 at 17:53
  • @MJD I don't understand what you are tying to say... I get these numbers as a result of an api call. The result set includes {max,sum,min,sumsq,count}. I was wondering if it was possible to calculate standard deviation using sumsq and count. – Akshat Jiwan Sharma Oct 27 '14 at 18:00
  • @barakmanos yes. – Akshat Jiwan Sharma Oct 27 '14 at 18:00
  • 1
    I am saying that if it is possible to calculate the standard deviation from just the sum of the squares, then any two sets of numbers which have the same sum-of-squares must have the same standard deviation. It is easy to find several sets of numbers which have the same sum-of-squares and check if they have the same standard deviation. If they do not, your question is answered straightaway. – MJD Oct 27 '14 at 18:22
  • @MJD Thanks. That clears it. – Akshat Jiwan Sharma Oct 27 '14 at 18:29

1 Answers1

1

You might note that e.g. $1^2 + 8^2 = 4^2 + 7^2$. Do $\{1,8\}$ and $\{4,7\}$ have the same standard deviation?

Robert Israel
  • 448,999