Standard Deviation

Σfx2 – x2

n

Σfx2 – Σfx 2

n n( )

OR

( )

( )

Value Frequency F * x FX * x

x F FX FXX

1 1    

2 3    

3 5    

4 4    

5 3    

6 2    

7 2    Σ      

1

12

14

6

15

16

15

98

72

75

64

45

12

1

20 79 367

Standard Deviation

Σfx2 – Σfx 2

Σf Σf( )( )

( - )36720

79 2

20( )

x F FX FXXΣ 20 79 367

Standard Deviation

Σfx2 – Σfx 2

n n( )( )

( - )36720

79 2

20( )(18.35 – 3.952)

Standard Deviation

Σfx2 – Σfx 2

n n( )( )

( - )36720

79 2

20( )(18.35 – 3.952) =(18.35- 15.6025)

Standard Deviation

Σfx2 – Σfx 2

n n( )( )

( - )36720

79 2

20( )(18.35 – 3.952) =(18.35- 15.6025)( 2.7475) = 1.66