Percentile
Apercentileis a comparison score between a particular score and the scores of the rest of a group. It shows the percentage of scores that a particular score surpassed. For example, if you scorepoints on a test, and are ranked in thethpercentile, it means that the scoreis higher thanof the scores.
The percentile rank is calculated using the formula
whereis the desired percentile andis the number of data points.
Example 1:
If the scores of a set of students in a math test are,,andwhat is the percentile rank of the score?
Arrange the numbers in ascending order and give the rank ranging fromto the lowest toto the highest.
Use the formula:
3
=
P
100
(
4
)
3
=
P
25
75
=
P
Therefore, the score
30
has the
75
thpercentile.
Note that, if the percentile rank
R
is an integer, the
P
thpercentile would be the score with rank
R
when the data points are arranged in ascending order.
If
R
is not an integer, then the
P
thpercentile is calculated as shown.
Let
I
be the integer part and be the decimal part of
D
of
R
. Calculate the scores with the ranks
I
and
I
+
1
. Multiply the difference of the scores by the decimal part of
R
. The
P
thpercentile is the sum of the product and the score with the rank
I
.
Example 2:
确定
35
thpercentile of the scores
7
,
3
,
12
,
15
,
14
,
4
and
20
.
Arrange the numbers in ascending order and give the rank ranging from
1
to the lowest to
7
to the highest.
Number
3
4
7
12
14
15
20
Rank
1
2
3
4
5
6
7
Use the formula:
R
=
35
100
(
7
)
=
2.45
The integer part of
R
is
2
, calculate the score corresponding to the ranks
2
and
3
. They are
4
and
7
. The product of the difference and the decimal part is
0.45
(
7
−
4
)
=
1.35
.
Therefore, the
35
thpercentile is
2
+
1.35
=
3.35
.