This document is a lesson on calculating quartiles, deciles, and percentiles from grouped and ungrouped data. It provides examples and step-by-step instructions on arranging data in ascending order and using the Mendenhall-Sincich method and formulas to determine the lower quartile, upper quartile, 5th decile, 50th percentile, and other values. It then provides practice problems for the student to solve involving grouped data from test scores and smoking levels. The document emphasizes rounding rules and identifying the correct interval before applying the formulas.

1. HEY, You!
DO YOU WANT
TO BE
MY BUDDY?
SUIT UP!
FOURTH QUARTER - WEEK 1
M10SP – IVa-1
RYAN REY L. SAJULGA
Author/Illustrator
HEY! I’m Detective Matt.
I have a new mission. My uncle Loc is
into solving problems that involve
measures of position. Do you want to
be my buddy? C’mon! Let’s help him!
But before doing so, we should revisit
this lesson first! Be vigilant to every
single information. Ready?

2. BE GUIDED!
There are two kinds of data that you will use, buddy:
GROUPED & UNGROUPED DATA.
UNGROUPED DATA—if the data are only few and
there is no need to transform the data into tabular form.
Examples:
1. 8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9
2. The test scores of 15 male students in Math.
GROUPED DATA—if the data is quite many, that is why
you need to make a table and form classes.
Examples:
1. 8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9, 7, 4, 8, 9, 3, 6, 7, 4, 8
11, 14, 4, 7, 4, 2, 8, 7, 9, 9, 9, 5, 5, 3, 4, 4, 12, 1, 4
2. The test scores of all males in DMMNHS in Math

3. In solving for Quartile, it is good for you to use a meth-
od called Mendenhall and Sincich Method.
Before everything else, arrange the elements in ascend-
ing order.
1. To use this, first, you need to calculate the lower
quartile (L). Where n is the number of
Elements
Round to the nearest integer. If L is between two num-
bers (0.5, 1.5, 2.5, etc.), round up.
2. Second, calculate for upper quartile (U).
Round to the nearest integer. If U is be-
tween two numbers (0.5, 1.5, 2.5, etc.), round down.
Example:
8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9, 4
Step 1: 1, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9
Step 2:
Therefore, the 3rd element is 3.
Step 3:
Therefore, the 10th element is 8.
Quartile 1 = 3
Quartile 2 = 5
Quartile 3 = 8
Buddy! To solve for the Deciles, remember these:
1. Arrange the elements in ascending order.
2. Use the formula, where n is the number
of elements, and round off to the near-
est integer.
Example: Find the 5th decile.
8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9, 4
Step 1: 1, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9
Step 2:
Therefore, after rounding up to the nearest integer, the
5th decile is the 7th element which is 5.
And now, I will show you how is Percentile to be solved!
1. Arrange the elements in ascending order.
2. Use the formula below, and round off to the nearest
integer.
Example: Find the 50th percentile.
8, 2, 5, 4, 8, 5, 7, 1, 3, 6, 9, 4
Step 1: 1, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9
Step 2:
Therefore, the 50th percentile is the 7th
element, which is 5.
Oops? Watch out buddy, there is
something that we can use.
Observe the 2nd quartile, 5th decile,
and 50th percentile. Do you see it?

4. COME ON! TRY THIS OUT...
Mr. Sajulga ask his Grade—10
Math students to ask at random 10
students in DMMNHS about their
ages. These are the data got by one
of his students.
Calculate for the 3rd quar-
tile, 5th decile, and 25th percentile.
Name Age Name Age
Ana 10 Tony 11
Jane 13 Lito 14
Susan 14 Christiam 13
Aneth 13 Michael 15
Gladys 15 John 12
ANOTHER HINT!
These are for grouped
data, buddy.

5. Lake Wood Rural Health Unit (RHU)
implements the “No Smoking Policy”
throughout the municipality. As part of the
campaign drive, they tested 40 smokers in
their nicotine levels.
Find for the 3rd quartile, 5th decile, and
75th percentile.
0 87 173 253 1 103 173 265 1 112
198 266 3 121 208 277 17 123 210 284
32 130 222 289 35 131 227 290 44 49
234 313 48 164 245 477 86 167 250 471
Class Intervals Frequency
Lower Bounda-
ries
Less than Cumu-
lative Frequency
420—479 2 419.5 40
360—419 0 359.5 38
300—359 1 299.5 38
240—299 9 239.5 37
180—239 6 179.5 28
120—179 8 119.5 22
60—119 4 59.5 14
0—59 10 -0.5 10
N = 40
3RD QUARTILE:
First, we need to find where the 3rd
quartile score is contained so that we will
know which class interval are we going
to use in the formula.
Therefore, the class interval that we
will use is 240—299 because it includes 29 to
37 scores (frequency). So, LB is 239.5; cfb is
28; fQk is 9; and i is 60.
Therefore, 75% of the 40 smokers, 3 in every 4 smokers,
have nicotine levels less than or equal to 252.8.
5TH DECILE:
First, we need to find where the 5th decile score is
contained so that we will know which class interval are
we going to use in the formula.
Therefore, the class interval that we will use is
120—179 because it includes 15 to 22 scores (frequency).
So, LB is 119.5; cfb is 14; fQk is 8; and i is 60.
Therefore, 50% of the 40 smokers, 2 in every 4 smokers,
have nicotine levels less than or equal to 164.5.

6. 75TH PERCENTILE:
First, we need to find where the 75th percentile
score is contained so that we will know which class inter-
val are we going to use in the formula.
Therefore, the class interval that we will use is
240—299 because it includes 29 to 37 scores (frequency).
So, LB is 239.5; cfb is 28; fQk is 9; and i is 60.
Therefore, 75% of the 40 smokers, 30 smokers, have
nicotine levels less than or equal to 252.8.
So? Have you
recorded all the de-
tails?
Again, before go-
ing into the general for-
mula, see to it you have
found already the class
interval where the
score (frequency) be-
longs.
Gather all the
things and leads you
have because I will let
you have the next, all
by yourself.
ARE YOU READY, BUDDY?
I KNOW YOU GOT THIS.
Dennis and Christine scored 32 and 23, respective-
ly, in the National Career Assessment Examination
(NCAE). The determining factor for a college scholarship
is that a student’s score should be in the top 10% of the
scores of his/her graduating class. In other words, their
scores should not fall into 90th percentile.
The students in the graduating class obtained the
following scores in the NCAE.
Can they apply for
the college scholarship?
NCAE
Scores
Fre-
quency
LB <CF
39-41 7
36-38 7
33-35 9
30-32 13
27-29 22
24-26 10
21-23 9
18-20 7
15-17 8
12-14 4
9-11 2
6-8 1
3-5 1
Note:
<CF is the accumulation of the fre-
quencies from the bottom up to the top.
Your <CF in the topmost should be equal to
your N or total examinees.

7. 1. What is N?
2. What is 90N/100?
3. Which score intervals does the score
above found?
4. What is the lower boundary and fre-
quency of that particular score interval?
5. What is the cumulative frequency of
the class intervals below the identified
interval?
6. What is the 90th percentile?
7. Do the scores of Dennis & Christine belong to 90th per-
centile?
ASSESSMENT
I already see a potential in
you of becoming a great Detective.
This will be my final test to you. If
you are successful in this task, I will
already allow you to help uncle Loc,
instead of me.
God bless!!!
RR is a grade—10 student. He has a daily allowance
of Php 15. He believes that 70% of his 59 classmates have
less than or equal to his daily allowance.
If the daily allowances of his whole class are as fol-
lows, do you agree with RR in his statement?
Why or why not?
Allowance
Intervals
Frequency
Less than Cumu-
lative Frequency
81—90 2 60
71—80 3 58
61—70 10 55
51—60 10 45
41—50 7 35
31—40 11 28
21—30 8 17
11—20 8 9
1—10 1 1

8. ANSWERS KEY
Buddy, kudos! Reaching this far is already a great
job.
This time, you compare your answers to this solu-
tions.
Therefore, the 5th decile is the 6th term, which is 13.
Therefore, the 3rd quartile is the 8th term, which is 14.
Therefore, the 25th percentile is the 3rd term, which is 12.
Since the 90th percentile is greater than the score of Dennis and
Christine, they cannot apply for the college scholarship.
I disagree with RR, because
70% of the whole class has less than or
equal to 57.5 or 58Php daily allow-
ance.
CASE CLOSED!!!
CONGRATULATIONS BUDDY. IT IS A VERY
NICE EXPERIENCE SOLVING CASE WITH YOU...
REFERENCES
http:www.mathisfun.com
http:www.google.com
Callanta, et. al.(2015).”Mathematics 10 Learner’s Module
(1st edition)”. Department of Education. Pasig City,
Philippines.
Bernabe, J., et. al.(2009).”Advanced Algebra, Trigonomet-
ry, and Statistics (Revised Edition)”. SD Publica—
tion, Inc. Quezon City, Philippines.