Find the standard deviation of first 21 natural numbers
Asked by admin @ in Math viewed by 352 People
Find the standard deviation of first 21 natural numbers.
Answered by admin @
Answer:
The standard deviation of first 21 natural number is √36.66
Step-by-step explanation:
We know that б = √ [Σxi²/n - (Σxi/n)²]
Σxi = [n * (n + 1)] / 2 .........(i)
Σxi² = [n * (n + 1) * (2n + 1)] / 6 .........(ii)
here, n = 21
now we have to put the value of n in equation (i) and (ii)
Σxi = ( 21 * 22 ) / 2 = 231
Σxi² = ( 21 * 22 * 43 ) / 6 = 3311
now ,
б = √ [ (3311 / 21) - (231/21)² ]
б = √ [ 157.66 - 11² ]
б = √ [ 157.66 - 121 ] = √36.66
So the standard deviation of first 21 natural number is √36.66
hope it helps
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