Question

The following are ages of 17 of the signers of the Declaration of Independence.

49, 34, 42, 43, 39, 36, 50, 44, 45, 33, 34, 27, 33, 69, 46, 50, 41
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Find 25th and 80th percentiles for these ages.
(If necessary, consult a list of formulas.)
(a) The 25th percentile:

The 80th
percentile:

Answer 1

Explanation:

The problem specifies that you may use a calculator. The formula, as reference, is:

1. Arrange n number of data points in ascending order: x1, x2, x3, ... xn
2. Calculate the rank r for the percentile p you want to find: r = (p/100) * (n - 1) + 1
3. If r is an integer then the data value at location r, xr, is the percentile p: p = xr

You can use a regular calculator or an online spreadsheet to solve. In sheets, arrange your data and use the =PERCENTILE( ) function. In the parentheses, write the range of your data and the requested percentile as a decimal. So if I type the data (the ages of the signers for this example) in cells A:4 through A:23, I'd write =percentile(A7:A23,0.25).

So the answers:

25th percentile is 34.

80th percentile is 48.4.