Why does the weighted sum of the standard deviations of the components making up the portfolio NOT equal to the portfolios standard deviation?

State of Nature	Returns per State of Nature for Each Security
RF	Market	w	x	y	z	Portfolio
Prob; Weights	16.67%	16.67%	16.67%	16.67%	16.67%	16.67%	100.00%
Good	20%	4.00%	14.00%	-1.00%	18.00%	10.00%	6.00%
Average	50%	4.00%	8.00%	6.00%	12.00%	6.20%	4.50%
Poor	30%	4.00%	2.00%	10.00%	-3.40%	3.30%	3.50%
Mean
Variance
Std Dev
beta
Required Return (CML)
CML efficient (Y/N)
Required Return (SML)
SML efficient (Y/N)
Mean Var Efficient Set

Covariance	RF	Market	w	x	y	z	Portfolio
RF
Market
w
x
y
z
Portfolio

Correlation	RF	Market	w	x	y	z	Portfolio
RF
Market
w
x
y
z
Portfolio

Matrix Multiplication for Portfolio Variance:

Weights' (1x6)

Variance/Covariance Matrix (6X6)

Weights (6x1)

Weights*Variance/Covariance matrix (1x6)

Weights (6x1)

Variance of Portfolio (1x1)

Standard Deviation of Portfolio