What are the changes that a sample size can change to standard deviation?

Answer 1

Consider that

x

d= x- Arithmetic mean

d2

1

1-1.5 = -0.5

0.25

2

2-1.5 = 0.5

0.25

=0.5

Arithmetic mean = (1+2)/2 =1.5

Standard deviation=

ie .5= 0.70

now Consider

x

d= x- Arithmetic mean

d2

1

1-2=-1

1

2

2-2=0

0

3

3-2=1

1

Arithmetic mean= (1+2+3)/3 = 2 =2

Standard deviation= = (2/2) = 1

So the Standard deviation can increase

now Consider

x

d= x- Arithmetic mean

d2

1

1-1.25=-0.25

0.0625

2

2-1.25=0.75

0.5625

1

1-1.25=-0.25

0.0625

1

1-1.25=-0.25

0.0625

Arithmetic mean= (1+2+1+1)/4= 1.25 = .75

Standard deviation= = (0.75/4) = 0.4330

So the Standard deviation can decrease

Standard deviation can either decrese or increase or remains the same