What is the Percentile
The usual percentile of P is the point or value that divides a data distribution into one hundred equal parts. Hence the percentile is often called the hundredth measure.
The dots that divide the distribution of data into one hundred equally large sections are the points: P1, P2, P3, P4, P5, P6, … and so on, up to P99. So here we find as many as 99 percentile points that divide the entire distribution of data into the same hundred sections, each of 1 / 100N or 1%.
To find the percentile used the formula as follows:
For single data:
Pn = 1 + (n / 10N – fkb)
For group data:
Pn = 1+ (n / 10N- fkb) xi
Pn = the nth percentile (here n can be filled with the numbers: 1, 2, 3, 4, 5, and so on up to 99.
1 = lower limit (real lower limit of scores or intervals containing the nth percentile).
N = number of cases.
Fkb = cumulative frequency located below the score or interval containing the nth percentile.
Fi = frequency of a score or interval containing the nth percentile, or its original frequency.
I = interval class or interval class.
1). An example of a decile calculation for a single data
Suppose we want to find the 5th percentile (P5), 20th percentile (P20), and 75th (P75), from the data presented in table 3.13 which has been calculated decile it. How to calculate it is as follows:
Ø Finding the 5th percentile (P5):
Point P5 = 5 / 10N = 5 / 10X60 = 3 (located at score 36). Thus we can know: 1 = 35.50; Fi = 2, and fkb = 1.
P5 = 1 + (5 / 10N-fkb) = 36.50 + (3-1)
Ø Finding the 75th percentile (P75):
Point P75 = 75 / 10N = 75 / 10X60 = 45 (lies on score 42). Thus we can know: 1 = 41.50; Fi = 8, and fkb = 40
P75 = 1 + (75 / 10N-fkb) = 41.50 + (45-40)
2). How to find percentiles for group data
Suppose again we want to find P35 and P95 from the data presented in table 3.14.
Ø Finding the 35th percentile (P35):
Point P35 = 35 / 100N = 35 / 100X80 = 28 (located at intervals 40-44). Thus we can know: 1 = 39.50; Fi = 15, and fkb = 20, i = 5
P35 = 1 + (35 / 100N-fkb) Xi = 39.50 + (45-40) X 5
= 39.50 + 2.67
Look for the 95th percentile (P95):
Point P95 = 95 / 100N = 95 / 100X80 = 76 (located at intervals 65-69). Thus we can know: 1 = 64.50; Fi = 5, and fkb = 72, i = 5
P95 = 1 + (95 / 100N-fkb) Xi = 64.50 + (65-69) X 5
= 64.50 + 4
The usefulness of percentiles in education is:
To change the swamp score (raw data) into standard score (default value).
In the world of education, one of the commonly used standard score is the eleven points scale (also known as the standard of eleven (standard value eleven) commonly abbreviated with the stanel.
The conversion from the raw score to the stanel is done by calculating: P1- P3- P8- P21- P39- P61- P79- P92- P97- and P99.
If the data we face is a normal curve (remember: the norm or standard is always based on the normal curve), then with the above 10 percentile point will get the standard values of 11 pieces, namely values 0, 1, 2, 3 , 4, 5, 6, 7, 8, 9, and 10.
Percentiles can be used to determine the position of a protégé, namely: on the percentile of how much the protégé earned his position in the middle of his group.
Percentiles can also be used as a tool for assigning passing limit values on a test or selection.
Suppose a total of 80 individuals as listed in Table 3.16. It will only be graduated by 4 people (= 4/80 X 100% = 5%) and that will not be passed is 76 people (= 76X80 X 100% = 95%), this means that P95 is the passing grade limit. Those whose values are at P95 down, are not graduated, while above P95 is passed. In the above calculation we have obtained P95 = 68.50; Means that can be passed are those whose value is above 68.50 is the value 69 and above.