Percentiles for Grouped Data:
Percentiles can also be calculated for grouped data which is done with the help of following formulae;

Where,
ℓ= lower boundary of the class containing the P₃₅ or P₉₉, i.e. the class corresponding to the cumulative frequency in which 35N/100 or 99N/100 lies
w= class interval size of the class containing P₃₅ or P₉₉.
f= frequency of the class containing P₃₅ or P₉₉.
N= number of values, or the total frequency.
‹C= cumulative frequency of the class preceding the class containing P₃₅ or P₉₉.

For Example:
We will calculate thirty-seventh, forty-fifth and ninetieth percentile from the frequency distribution of weights of 120 students, by using the this table.

=182.83 pounds
Conclusion
From P₃₇, P₄₅ and P₉₀ we have concluded or interpreted that 37% student weigh 147.5 pounds or less. Similarly, 45% students weigh 151.1 pounds or less and 90% students weigh 182.83 pounds or less.

Big Example:
Find the percentiles P₈, P₅₀, and P₈₅ of the following data.

Columns Load	Frequency
50-69	3
70-89	7
90-109	4
110-129	4
130-149	9

Solution:
1) find each cumulative frequency and each real interval.

2) Remember the percentile common formula of continuous or discrete distribution (Grouped Data).

ℓ= the lower boundary of relevant percentile class
‹C= the cumulative frequency of the previous interval of relevant percentile class
f= the frequency of relevant percentile class
w= the length of the real interval
4) find eighth percentile.

5) find fiftieth percentile.

6) find eighty-fifth percentile.

7) Find the percentile number of the estimated datum of 115 in the above data.

ℓ= the lower boundary of related percentile class=109.5
‹C= the cumulative frequency of the previous interval of related percentile class=14
f= the frequency of related percentile class=4
w= the length of the real interval =20

then X=15.1, then the percentile number

Let’s read post Calculation of Quartiles, Deciles & Percentiles for Grouped Data.