Question

calculate 67th percentile of the following sample

-2.1

-0.3

0.4

1.2

1.5

2.1

2.2

3.3

4.0

5.0

Answer 1

We need to compute the 67% percentile based on the data provided.

Position	X (Asc. Order)
1	-2.1
2	-0.3
3	0.4
4	1.2
5	1.5
6	2.1
7	2.2
8	3.3
9	4.0
10	5.0

The next step is to compute the position (or rank) of the 67% percentile. The following is obtained:

Since the position found is not integer, the method of interpolation needs to be used. The 67% percentile is located between the values in the positions 7 and 8. Those values, based on the data organized in ascending order, are 2.2 and 3.3.

The value of 7.37 - 7 = 0.37 corresponds to the proportion of the distance between 2.2 and 3.3 where the percentile we are looking for is located at. In fact, we compute

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