In a sample of data, the frequencies of $1,2,3,4$ are $p _ { 1 } , p _ { 2 } , p _ { 3 } , p _ { 4 }$ respectively, and $\sum _ { i = 1 } ^ { 4 } p _ { i } = 1$ . Among the following four cases, the one with the largest standard deviation is
A. $p _ { 1 } = p _ { 4 } = 0.1 , p _ { 2 } = p _ { 3 } = 0.4$
B. $p _ { 1 } = p _ { 4 } = 0.4 , p _ { 2 } = p _ { 3 } = 0.1$
C. $p _ { 1 } = p _ { 4 } = 0.2 , p _ { 2 } = p _ { 3 } = 0.3$
D. $p _ { 1 } = p _ { 4 } = 0.3 , p _ { 2 } = p _ { 3 } = 0.2$