Sampling distribution of median

Questions where the statistic is the median of the sample (requires ordering sample values and finding middle value).

2 questions

Edexcel S2 2013 June Q1
  1. A bag contains a large number of \(1 \mathrm { p } , 2 \mathrm { p }\) and 5 p coins.
    \(50 \%\) are 1 p coins
    \(20 \%\) are \(2 p\) coins
    30\% are 5p coins
    A random sample of 3 coins is chosen from the bag.
    1. List all the possible samples of size 3 with median 5p.
    2. Find the probability that the median value of the sample is 5 p .
    3. Find the sampling distribution of the median of samples of size 3
Edexcel S2 2015 June Q7
  1. A bag contains a large number of \(10 \mathrm { p } , 20 \mathrm { p }\) and 50 p coins in the ratio \(1 : 2 : 2\)
A random sample of 3 coins is taken from the bag.
Find the sampling distribution of the median of these samples.