Question

find the standard deviation of first 21 natural Number

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Answer 1

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