Question

Find 10-th, 60-th and 75-th percentiles in each of your data set, then write down each value that corresponds to those percentiles. Now use those values to find sample percentiles empirically (Suppose value “a” corresponds to 10-th percentile in my data set. After finding the value “a” forget about the 10-th percentile, use only the data set to find value “a” corresponds to which percentile in my data set. Suppose I found the percentile value as “X”, is there any difference between “X” and 10? Should they be equal to each other? ). Are there any differences between the percentile values corresponding to the same observation in the data? If there exists any difference, what could be the reason. Also compare the findings in terms of 2 different data sets.