The following are the P/E ratios (price of stock divided by projected earnings per share) for 16 banks.
19,15,43,22,18,25,29,18,19,34,22,15,24,14
Find 25th and 90th percentiles for these ratios
Put the values in order from lowest to highest.
25th percentile will have 1/4 of the data below that number.
90th will have .9 of the data below that nu
To find the 25th and 90th percentiles for the given P/E ratios, you need to first organize the ratios in ascending order. Then, you can use the formulas to calculate the specific percentiles.
Here is the list of the given P/E ratios in ascending order:
14, 15, 15, 18, 18, 19, 19, 22, 22, 24, 25, 29, 34, 43
To find the 25th percentile, you can use the formula:
25th Percentile = (25/100) * (n + 1)
where n is the total number of data points.
In this case, n = 14, so the calculation would be:
25th Percentile = (25/100) * (14 + 1) = (25/100) * 15 = 0.25 * 15 = 3.75
Given that the 25th percentile position falls between the 3rd and 4th values, you need to interpolate to get the exact value.
Interpolation formula:
25th Percentile = Value at (3rd position) + (0.75 * (Value at (4th position) - Value at (3rd position)))
In this case, the value at the 3rd position is 15, and the value at the 4th position is 18.
Using the interpolation formula:
25th Percentile = 15 + (0.75 * (18 - 15)) = 15 + (0.75 * 3) = 15 + 2.25 = 17.25
Therefore, the 25th percentile for the given P/E ratios is approximately 17.25.
Now, to find the 90th percentile, you can use the same approach:
90th Percentile = (90/100) * (n + 1)
In this case:
90th Percentile = (90/100) * 15 = 0.9 * 15 = 13.5
Given that the 90th percentile position falls between the 13th and 14th values, you need to interpolate to get the exact value.
In this case, the value at the 13th position is 29, and the value at the 14th position is 34.
Using the interpolation formula:
90th Percentile = 29 + (0.5 * (34 - 29)) = 29 + (0.5 * 5) = 29 + 2.5 = 31.5
Therefore, the 90th percentile for the given P/E ratios is approximately 31.5.
So, the 25th percentile is approximately 17.25, and the 90th percentile is approximately 31.5.