Question

This is my rough working for part a. My question is for empirical distribution after ranking them if they are the same do we rank them as the same number rank or as I did. The textbook was Xi less than & equal to Xi+1 but the graph looks weird to me.

For part b 0.25percentile is in the middle of 0.2 and 0.3 will it be 49? What kind of presentation of working would be appropriate?

5. (20 marks) Suppose we have a random sample of n 10 observations as in the following 50 66 59 49 15 4 59 72 83 117 (a) Obtain the EDF from this data set. (b) Obtain the 0.25th, 0.5th and the 0.75th sample quantiles.

Answer 1

As there are 10 observation so after sorting data which is

4  15  49  50  59  59  66  72  83 117

we can find the 0.25th percentile as 10(0.25) = 2.5 th observation i.e 3rd observation which is 49.
simalarly for 0.5th and 0.75th percentile we have to take 5th and 7.5th (~8th) obsevation which is 59 and 72. so

    25%  50%  75%  
    32   59   69