Standard deviation changes?

You 'must' know the old standard deviation to find the new standard deviation.
Mean = ∑x / n
n=15
mean = 25
∑x (old) = 25*15 = 375
∑x (new) = 375-12.9+1.29 = 363.39

Variance = (∑x^2 - ( ∑ x)^2 / n ) / (n-1)
Let the old standard deviation be 2.5 (assume)
Then, old variance = (2.5)^2 = 6.25

(∑x^2 - ( ∑ x)^2 / n ) / (n-1) = 6.25
(∑x^2 - ( 375)^2 / 15 ) / 14 = 6.25
multiply both sides by 14
(∑x^2 - ( 375)^2 / 15 ) = (6.25)(14)
(∑x^2 - ( 375)^2 / 15 ) = 87.5
∑x^2 (old) = 87.5 + ( 375)^2 / 15
∑x^2 (old) = 9462.5
∑x^2 (new) = 9462.5 -(12.9)^2 + (1.29)^2
∑x^2 (new) = 9297.7541
∑x (new)= 363.39
n = 15 (unchanged)

Use variance formula with the new numbers
Variance = (∑x^2 - ( ∑ x)^2 / n ) / (n-1)
Variance = (9297.7541 - ( 363.39)^2 / 15 ) / 14
= 35.3049
New standard deviation = sqrt(35.3049) = 5.9418

The standard deviation changed by 5.9418 - 2.5 = 3.4418 (increased)
Percentage increase = (2.5/3.4418)*100 = 72.63%


You may want to use this technique only when you don't have the original data but know
what the old standard deviation was (and the old mean was).
Otherwise, you may simply recompute the new standard deviation.