median can give incorrect answer for Binomial distribution

[marcusps]

For some reason median(Binomial(25,0.3)) is different from quantile(Binomial(25,0.3),0.5) or any other method of computing the median

julia> median(Binomial(25,0.3))
8

julia> quantile(Binomial(25,0.3),0.5)
7

julia> [(n,cdf(Binomial(25,0.3),n)) for n in 0:10]
11-element Vector{Tuple{Int64, Float64}}:
 (0, 0.00013410686196639642)
 (1, 0.0015709660973206466)
 (2, 0.0089605278791425)
 (3, 0.033240516590842865)
 (4, 0.09047191855413662)
 (5, 0.1934884420880652)
 (6, 0.340654904279392)
 (7, 0.5118485439713417)
 (8, 0.6769281251028678)
 (9, 0.8105639764950546)
 (10, 0.9021999888782681)
 
 julia> [(n,sum(pdf(Binomial(25,0.3),0:n))) for n in 0:10]
11-element Vector{Tuple{Int64, Float64}}:
 (0, 0.0001341068619663966)
 (1, 0.001570966097320648)
 (2, 0.008960527879142505)
 (3, 0.03324051659084287)
 (4, 0.09047191855413667)
 (5, 0.19348844208806526)
 (6, 0.34065490427939144)
 (7, 0.5118485439713427)
 (8, 0.6769281251028665)
 (9, 0.8105639764950529)
 (10, 0.9021999888782666)

julia> quantile([rand(Binomial(25,0.3)) for _ in 1:100_000_000],0.5)
7.0

and the issue is not special to Binomial(25,0.3)

julia> [(n,median(Binomial(n,0.3)),quantile(Binomial(n,0.3),0.5)) for n in 0:5:100]
21-element Vector{Tuple{Int64, Int64, Int64}}:
 (0, 0, 0)
 (5, 2, 1)
 (10, 3, 3)
 (15, 4, 4)
 (20, 6, 6)
 (25, 8, 7)
 (30, 9, 9)
 (35, 10, 10)
 (40, 12, 12)
 (45, 14, 13)
 (50, 15, 15)
 (55, 16, 16)
 (60, 18, 18)
 (65, 20, 19)
 (70, 21, 21)
 (75, 22, 22)
 (80, 24, 24)
 (85, 26, 25)
 (90, 27, 27)
 (95, 28, 28)
 (100, 30, 30)