The standard deviation of the data is 1.8
X ____ 0 __ 1 __ 2 __ 3 __ 4 __ 5
P(X) _ 0.2 _ 0.1 _ 0.1 _ 0.2_ 0.2 _ 0.2
The standard deviation is defined as :
Var(X) = ∑x² *p(x) - E(X)²
E(X) = ∑x*p(x)
E(X) = (0*0.2) + (1*0.1) + (2*0.1) + (3*0.2) + (4*0.2) + (5*0.2)
E(X) = 2.7
∑x² * p(x) = (0²*0.2) + (1²*0.1) + (2²*0.1) + (3²*0.2) + (4²*0.2) + (5²*0.2) = 10.5
Var(X) = 10.5 - 2.7²
Var(X) = 3.21
Std(X) = √3.21
Std(X) = 1.79 ≈ 1.8
Complete Question:
Find the standard deviation of the following data. Round your answer to one decimal place. x 0 1 2 3 4 5 P(X) 0.2 0.1 0.1 0.2 0.2 0.2