Problem 5E

Refer to Exercise 5.3. Assume that a random sample of n = 2 measurements is randomly selected from the population.

a. List the different values that the sample median m may assume and find the probability of each. Then give the sampling distribution of the sample median.

b. Construct a probability histogram for the sampling distribution of the sample median and compare it with the probability histogram for the sample mean (Exercise 5.3, part b).

Solution :

Step 1 of 2:

We assume that a random sample of n=2 measurements is randomly selected from the population.

Our goal is :

a). We need to list the different values that the sample median and we have to find the probability

of each.

b). We need to construct histogram for the sampling distribution of the sample median and compare it with the probability histogram for the sample mean.

a). Now we have to list the different values that the sample median

Then we have to find the probability of each. Then give the sampling distribution of the sample median.

We know that sample size n is 2.

Then the sample median table is given below.

Sample |
Observation 1 |
Observation 2 |
Median (m) |
Probability |

1 |
1 |
1 |
1 |
0.04 |

2 |
1 |
2 |
1.5 |
0.06 |

3 |
1 |
3 |
2 |
0.04 |

4 |
1 |
4 |
2.5 |
0.04 |

5 |
1 |
5 |
3 |
0.02 |

6 |
2 |
1 |
1.5 |
0.06 |

7 |
2 |
2 |
2 |
0.09 |

8 |
2 |
3 |
2.5 |
0.06 |

9 |
2 |
4 |
3 |
0.06 |

10 |
2 |
5 |
3.5 |
0.03 |

11 |
3 |
1 |
2 |
0.04 |

12 |
3 |
2 |
2.5 |
0.06 |

13 |
3 |
3 |
3 |
0.04 |

14 |
3 |
4 |
3.5 |
0.04 |

15 |
3 |
5 |
4 |
0.02 |

16 |
4 |
1 |
2.5 |
0.04 |

17 |