Math 10 PERCENTILE RANK of GROUPED DATA.pptx

CLASSROOM RULES
L - Listen carefully and attentively to others.
E - Encourage and support your classmates.
A - Act responsibly and respectfully.
R - Respect everyone and the environment.
N - Never give up on trying your best.
ALWAYS REMEMBER TO LEARN!

REVIEW
1. What was our last lesson?
2. What are deciles?
3. What is the formula in calculating
the decile of grouped data?

Deciles are the 9 score points
that divides the distribution into
ten equal parts.

• Are you familiar
with what on the
pictures are?

The four Sanggre's who are Pirena, Amihan,
Alena and Danaya are seen to love each other.
Until…

Minea the mother of the four Sang’gres decides
Amihan will be the new elected queen of Lireo. Pirena
felt jealous and angry towards Amihan. With that she
left the Kingdom.
Oh, Noooo…

In order to get back
Pirena to the
Kingdom, we must
help Lira the daughter
of Amihan as she is
hailed as the savior of
four sanggre’s, who
hate each other.
WILL YOU HELP LIRA?

• There are three
quests that
needs to be
done in order
to get back
Pirena to the
Kingdom. In
every quests
there will be a
reward for
those who
succeed in
winning back
Pirena’s heart.

Quest 1: WORD QUEST
 Each group will be assigned to
a picture
 Write the word or phrase depicted
by the picture.
(Word or phrase are related to the
new lesson)
 After one minute, each group will
simultaneously show the words/phrase
they have written on the provided
answer sheet.

Group I
Group II
Group III Group IV
POSITION
MEASURE
GROUPED PERCENTILE FORMULA

MEASURES OF
POSITION
PERCENTILES FOR
GROUPED DATA
RAPHAEL V. PEREZ

THE PERCENTILE FOR
GROUPED DATA
The percentile of grouped data is used to
characterize values according to the
percentage below them.
Measures of Position: Percentile for Grouped Data
These are the 99 score points that divides
the distribution into 100 equal parts.

Early on, you have already learned that:
• kth quartile denoted by Qk ,
• kth decile denoted by Dk ,
are computed, respectively, as follows:
Qk = LB +
(𝑘
4
𝑁)- cfb
fQK
i
Dk = LB +
(𝑘
10
𝑁 ) -cfb
fDK
i
and

What will be the formula for the kth
percentile?
Qk = LB +
(𝑘
4
𝑁)- cfb
fQK
i Dk = LB +
(𝑘
10
𝑁 ) -cfb
fDK
i
and
if:
Pk = LB +
( 𝑘
𝟏𝟎𝟎
𝑁) - cfb
fPK
i
Then,

THE kth PERCENTILE FORMULA FOR
GROUPED DATA
Pk = LB +
( 𝑘
𝟏𝟎𝟎
𝑁) - cfb
fPK
i
LB = lower boundary of the kth percentile class
total frequency
cfb = cumulative frequency before the percentile class
fPK = frequency of the percentile class
i = the interval or class width
nth percentile where = 1, 2, 3,…..97, 98 and 99
Where:

To determine the percentile class in the
Frequency Distribution Table:
Step 1: Compute for the Position to determine
percentile class
𝑘
𝟏𝟎𝟎
𝑁
Position of PK :
Step 2: Set the given facts for the identified
Percentile Class.
Like :
LB - the lower boundary of a percentile class
cfb - cumulative frequency before the percentile class
- the position of a percentile class
fPK - frequency of a percentile class
i - the class width or interval

To determine the percentile class in the
Frequency Distribution Table:
Step 3: Set the formula and substitute the variables
using the given facts and then, evaluate.
Step 4: Write the analysis of the value of the
Percentile Class

Example: Calculate the 65th
and 32nd
Percentile of the Mathematics Test
Scores of 50 Students.
SCORES
(Class Interval)
Frequency
(f)
46-50 4
41-45 8
36-40 11
31-35 9
26-30 12
21-25 6

Calculate the 65th
Percentile of the
Mathematics Test Scores of 50
Students.

Solution:
Step 1: Complete the Frequency Distribution Table
SCORES
(Class Interval)
Frequency
(f)
LB <cf
46-50 4 45.5 50
41-45 8 40.5 46
36-40 11 35.5 38
31-35 9 30.5 27
26-30 12 25.5 18
21-25 6 20.5 6
N = 50
LB <cf
(21 – 1) + 0.5
(26 – 1) + 0.5
(31 – 1) + 0.5
(36 – 1) + 0.5
(41 – 1) + 0.5
(46 – 1) + 0.5
6 - Set the
value of
frequency
from the
lowest class
6+12
18+9
27+11
38+8
46+4

Compute for the Position of the 65th Percentile
Class or P65
SCORES
(Class Interval)
Frequency
(f)
LB <cf
46-50 4 45.5 50
41-45 8 40.5 46
36-40 11 35.5 38
31-35 9 30.5 27
26-30 12 25.5 18
21-25 6 20.5 6
N = 50
65
100
𝑁
Position of P65 :
:
:
:32.50th
The 32.50th
position is between
the cumulative
frequency 27th and
38th. Use the class
36-40
P65

Step 2: Set the given facts for 65th Percentile
Class or P65
SCORES
(Class Interval)
Frequency
(f)
LB <cf
46-50 4 45.5 50
41-45 8 40.5 46
36-40 11 35.5 38
31-35 9 30.5 27
26-30 12 25.5 18
21-25 6 20.5 6
N = 50
P65
Given:
LB = 35.5
N = 50
cfb = 27
fP65 = 11
i = 5
cfb =
LB =
fP65 =

Step 3 and 4: Set the formula for P65 ,substitute and
evaluate. Write the final answer and put the
analysis.
Given:
LB = 35.5
N = 50
cfb = 27
fP65 = 11
i = 5
Pk = LB +
( 𝑘
𝟏𝟎𝟎
𝑁) - cfb
fPK
i
Formula:
P65 = 35.5 +
( 65
𝟏𝟎𝟎
⋅50)- 27
11
5

P65 = 35.5 +
32.5 - 27
11
5
P65 = 35.5 +
5.5
11
5
P65 = 35.5 + 0.5 5
P65 = 35.5 + 2.5
P65 = 38.0
Analysis:
65% of the students got a score
below 38 and 35% of the students
got a score above 38.

Calculate the 32nd Percentile of the
Mathematics Test Scores of 50
Students.

Compute for the Position of the 32nd Percentile
Class or P32
SCORES
(Class Interval)
Frequency
(f)
LB <cf
46-50 4 45.5 50
41-45 8 40.5 46
36-40 11 35.5 38
31-35 9 30.5 27
26-30 12 25.5 18
21-25 6 20.5 6
N = 50
32
100
𝑁
Position of P32 :
:
:
:16th
The 16th position is
between the
cumulative
frequency 6th and
18th. Use the class
26-30
P32

Set the given facts for 32nd Percentile Class or P32
SCORES
(Class Interval)
Frequency
(f)
LB <cf
46-50 4 45.5 50
41-45 8 40.5 46
36-40 11 35.5 38
31-35 9 30.5 27
26-30 12 25.5 18
21-25 6 20.5 6
N = 50
P32
Given:
LB = 25.5
N = 50
cfb = 6
fP32 = 12
i = 5
cfb =
LB =
fP32 =

Set the formula for P32 ,substitute and evaluate.
Write the final answer and put the analysis.
Given:
LB = 25.5
N = 50
cfb = 6
fP32 = 12
i = 5
P32 = 25.5 +
( 32
𝟏𝟎𝟎
⋅50)- 6
12
5
P32 = 25.5 +
16 - 6
12
5
P65 = 25.5 +
10
12
5
P65 = 25.5 + 0.833 5
P65 = 25.5 + 4.167
P32 = 29.667 29.67
Analysis:
32% of the students
got a score below
29.67 and 68% of
the students got a
score above 29.67.

Quest 3: Calculate for the following using the same
data and write the analysis.
SCORES
(Class Interval)
Frequency
(f)
LB <cf
46-50 4 45.5 50
41-45 8 40.5 46
36-40 11 35.5 38
31-35 9 30.5 27
26-30 12 25.5 18
21-25 6 20.5 6
N = 50
For G1 and G3 P70 and G2 and G3: P40

P70 = 39.14 P40 = 31.61
Analysis:
below 39.14 and 30% of the
students got a score above 39.14.
Analysis:
below 31.61 and 60% of the
students got a score above 31.61.
ANSWERS:

Real – Life Application
Percentiles are commonly used in
various fields, including education,
healthcare, and finance, to assess
and compare individual
performances or values within a
larger population

GENERALIZATION:
In computing the percentiles of grouped data, the following
formula is used:
Pk = LB +
( 𝑘
𝟏𝟎𝟎
𝑁) - cfb
fPK
i
LB = lower boundary of the kth percentile class
total frequency
cfb = cumulative frequency before the percentile class
fPK = frequency of the percentile class
i = the interval or class width
nth percentile where n = 1, 2, 3,…..97, 98 and 99
Where:

ASSESSMENT:
https://forms.office.com/r/pwUAz5WC90

STUDY
PERCENTILE RANK
GROUPED DATA

Math 10 PERCENTILE RANK of GROUPED DATA.pptx

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