Step 1 :Given the P/E ratios for 16 banks are: 18, 14, 22, 18, 19, 23, 29, 21, 15, 20, 14, 23, 43, 17, 23, 29.
Step 2 :First, sort the data in ascending order: 14, 14, 15, 17, 18, 18, 19, 20, 21, 22, 23, 23, 23, 29, 29, 43.
Step 3 :The percentile of a set of values is the value below which a certain percent of the observations fall. For example, the 10th percentile is the value below which 10% of the observations may be found.
Step 4 :To find the 10th and 75th percentiles, we can find the values at the corresponding positions in the sorted list. The position of the nth percentile in a sorted list of p observations is given by \((n/100)*p\). If this is not an integer, we round up to the nearest integer.
Step 5 :Using this formula, we find that the 10th percentile of the data is 14.5 and the 75th percentile is 23.0. These are the values below which 10% and 75% of the observations may be found, respectively.
Step 6 :Final Answer: \(\boxed{14.5}\) is the 10th percentile and \(\boxed{23.0}\) is the 75th percentile.