Percentile - Alternative Methods

Alternative Methods

Some software packages, including Microsoft Excel (up to the version 2007) use the following method, noted as an alternative by NIST to estimate the value, of the P-th percentile of an ascending ordered dataset containing N elements with values .

The rank is calculated:

and then split into its integer component k and decimal component d, such that . Then is calculated as:

v_P = \begin{cases} v_1, & \mbox{for }n=1 \\ v_N, & \mbox{for }n=N \\ v_k+d(v_{k+1}-v_k), & \mbox{for }1 < n < N \end{cases}

The primary method recommended by NIST is similar to that given above, but with the rank calculated as

These two approaches give the rank of the 40th percentile in the above example as, respectively:

and

.

The values are then interpolated as usual based on these ranks, yielding 29 and 26, respectively, for the 40th percentile.

Read more about this topic:  Percentile

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