Percentile Formula with Solved Examples

Percentile Formula

Percentile and % are sometimes misunderstood terms. However, they are not the same thing. Percentiles are the figures under which a specific proportion of the data set is discovered. In contrast, percentages are the numbers under which a given per cent of the data from a data set is obtained. If you want to know what’s happening about the entire crowd, you’ll need a percentile figure indicating relative standing.

The percentile formula is given by:

Percentile = (n/N) x 100

n = a given value’s ordinal rank

N  = the total number of items in the data collection

To analyse and evaluate data, we utilise the word percentile within mathematics. Unofficially, it can also mean that a specific proportion is below a certain percentile figure.

Percentiles are useful in comprehending numbers such as exam scores, health outcomes, and other metrics in daily life. If you finish within the 25th percentile, we will be in the bottom 25% of examinees for illustration. The ranking is 25 in this case. A data set is divided into 100 equal sections by a percentile.

A percentile is a statistic that informs us what percentage of a data set’s overall frequency falls inside that range.

Solved Examples

1. Consider the following percentage problem: A listing of scores for 15 pupils has been announced in a university. 85, 34, 42, 51, 84, 86, 78, 85, 87, 69, 74, 65 represent respective scores. How do you calculate the 80th percentile?

1st step:

Sort the information in ascending order.

Let’s do it this way: 34, 42, 51, 65, 69, 74, 78, 84, 85, 85, 86, 87, 84, 85, 85, 85, 86, 87.

2nd step:

Locate Rank,

Rank = Percentile/100

= 80/100

K = 0.80

3rd step:

Locate the 80th percentile,

80th percentile = 0.80*12

= 9.6

4th Step:

Round to the closest whole number because it isn’t a whole number.

As a result, 9.6 is rounded up as 10.

Tally the numbers in the above set of data sets left to right unless you find the number 10.

The tenth number in the provided data set seems to be 85.

As a result, the data set’s 80th percentile equals 85.

Important Formulas: