The following are the P/E ratios (price of stock divided by projected earnings per share) for 16 banks.
\[
18,14,22,18,19,23,29,21,15,20,14,23,43,17,23,29
\]
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Find $10^{\text {th }}$ and $75^{\text {th }}$ percentiles for these ratios.
(if necessary, consutt a tist of tormulas.)
(a) The $10^{\text {th }}$ percentile: 1
(b) The $75^{\text {th }}$ percentile:

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.