Business Statistics

Chapter 4 | Measures of Dispersion 131

tabLe 4.6

Computation of standard deviation and variance for Example 4.2

x f f

.x

(

x

i

–

x

) (

x

i

–

x

)

2

f

i

(x

i

–

x

)

2

10 8 80 –2.13 4.5369 36.2952

11 10 110 –1.13 1.2769 12.769

12 16 192 –0.13 0.0169 0.2704

13 20 260 0.87 0.7569 15.138

14 4 56 1.87 3.4969 13.9876

15 2 30 2.87 8.2369 16.4738

Sum 60 728 94.934

728

Arithmetic mean ( ) = 12.13

60

fx

x

f

= =

∑

∑

2

1

( )

94.934

Standard deviation( ) 1.26

1 59

=

−

= = =

−

∑

n

i i

i

f x x

s

N

2

2

1

( )

94.934

Variance( ) 1.60

1 59

=

−

= = =

−

∑

n

i i

i

f x x

s

N

4.4.16 Using MS Excel for Computing Standard Deviation

For an individual series, the Data Analysis dialog box (Figure 3.4), discussed in Chapter 3,