Question

Calculate the mean and standard deviation of first n

natural numbers.​

Answer 1

Step-by-step explanation:

11th

Maths

Statistics

Variance and Standard Deviation

Standard Deviation of first...

STATISTICS

Standard Deviation of first n natural numbers.

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ANSWER

Mean, u=

n

(1+2+3...+n)

∴u=

2

1

(n+1)

Variance, σ

2

=

n

∑(x

i

−u)

2

=

n

∑x

i

2

−u

2

∴σ

2

=

n

∑n

2

−

2

1

(n+1)

2

∴σ

2

=

n

1

n

n(n+1)(2n+1)

−(

2

1

(n+1))

2

∴σ

2

=

12

n

2

−1

Standard Deviation, S.D=

σ

2

∴S.D=\sqrt{\dfrac{n^2-1}{12}}