# Thread: median of a sampling distribution

1. ## median of a sampling distribution

hi i'm a bit confused on a simple question which i thought i did correct, but the mark scheme has a different answer.

A bag contains a large number of coins:
75% are 10p coins,
25% are 5p coins.

A random sample of 3 coins is drawn from the bag.
Find the sampling distribution for the median of the values of the 3 selected coin
s

and the answer is:

Median 5: p = (0.25)^3 + 3(0.75)(0.25)^2 = 10/64

Median 10: p = (0.75)^3 + 3(0.25)(0.75)^2 = 54/64

so basically they are using the case for median 5 with 2 5's or 3 5's, but these are the combinations:

Median 5: (5 5 5) (5 5 10) (10 5 10) (10 5 5)

Median 10: (10 10 10) (5 10 10) (10 10 5) (5 10 5)

why are the combinations i've shown in red used the other way around?

2. Originally Posted by Aquafina
hi i'm a bit confused on a simple question which i thought i did correct, but the mark scheme has a different answer.

A bag contains a large number of coins:
75% are 10p coins,
25% are 5p coins.

A random sample of 3 coins is drawn from the bag.
Find the sampling distribution for the median of the values of the 3 selected coin
s

and the answer is:

Median 5: p = (0.25)^3 + 3(0.75)(0.25)^2 = 10/64

Median 10: p = (0.75)^3 + 3(0.25)(0.75)^2 = 54/64
median(med) is discrete rv. It takes the values 5 and 10.
we have
$p\{med =5\}=$
P{ we draw two coins 5p, one coin 10p}+P{we draw all of coins 5p}
$C_3^2(0.25)^2 (0.75) +(0.25)^3$
(because three drawing coins are independent)
similar, we get p{med =10}

3. Originally Posted by Aquafina
Median 5: (5 5 5) (5 5 10) (10 5 10) (10 5 5)

Median 10: (10 10 10) (5 10 10) (10 10 5) (5 10 5)

why are the combinations i've shown in red used the other way around?
the combination (10 5 10) have median 10. For getting the median, the first step we have to order from low to higher. The combination (5, 10 5) have median 5.
Median - Wikipedia, the free encyclopedia

4. thanks! seems like a stupid question now, but the ordering didn't hit me then.

Thanks