Topic: MEASURES OF POSITION
Measures of position are used to
describe the position of a data value
in relation to the other data. The
most frequent measures of positions
are quartiles, deciles, and percentiles.
1. QUARTILES are the score points which
divide a distribution into four equal parts.
Each set of data has three quartiles.
a. First Quartile (Q1)=is a number such
that at most one-fourth or 25% of the data
are smaller in value than Q1, and at most
three-fourths or 75% are larger. It is
sometimes called the lower quartile.
b. Second Quartile (Q2)= is a number
such that one-half or 50% of the data are
below and above in value than Q2. Second
quartile is obviously the median.
c. Third Quartile (Q3)= is a number
such that at most three-fourths or 75% of
the data are smaller in value than Q3, and
at most one-fourth or 25% are larger. It
is sometimes called the upper quartile.
The difference between Q1 and Q3 is called
the interquartile range.
Quartiles can be represented into diagram when
the data is arranged in increasing order.
25%
25%
25%
25%
H
L
Q1
Q2
Q3
LOWER
QUARTILE
MEDIAN
UPPER
QUARTILE
a. 25% of the data has a value ≤ 𝑄1
b. 50% of the data has a value ≤ 𝑄2
c. 75% of the data has a value ≤ 𝑄3
DECILES are the nine score points that
divide a distribution into ten equal parts.
D1=is the score which has 10% of the
scores below it and 90% above it.
D2=is the score which has 20% of the
scores below it and 80% above it.
D3=is the score which has 30% of the
scores below it and 70% above it.
D4=is the score which has 40% of the
scores below it and 60% above it.
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D9=is the score which has 90% of the
scores below it and 10% above it.
3. PERCENTILES are the ninety-nine
score points which divide a distribution into
one hundred equal parts, so that each part
represents the data set. It is used to
characterize values according to the
percentage below them.
P1 separates the lowest 1% from the other 99%.
P2 separates the lowest 2% from the other 98%.
P3 separates the lowest 3% from the other 97%.
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P99 separates the lowest 99% from the other 1%.
Illustrative Examples
1. How many percent corresponds to Q3 if
you will interpret it?
Answer: 75% of the data have a value less
than or equal to Q3.
2. Aldrin is an IT expert in one big
company. His salary is in the 8th decile.
Should Aldrin be glad about his salary or
not?
Answer: 80% of the employees receive a
salary that is less than or equal to his
salary and 20% of the employees receive a
salary that is greater than his salary. Aldrin
should be pleased with his salary.
3. There are 11 data items. 2, 4, 5, 6, 6, 7,
8, 9, 9, 10, 11.
The median or Q2 is the 6th item. So Q2 = 7
The lower quartile is the 3rd item.So Q1 = 5
The upper quartile is the 8th item.So Q3= 9
What do the information above mean?
Answer:
2, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11
Q1
Q2 Q3
25% of the data have a value that is less than
or equal to 5.
50% of the data have a value that is less than
or equal to 7.
• 75% of the data have a value that is less than
or equal to 9.
4. Below is the table showing the ages of 15
students in Camantiles NHS.
Name Age Name Age
Name Age
Joseph 13
Anne
14
Jaimie 14
Lea
12
Chito 16
Maye
12
Tina
15
Dave
15
Ruben 17
Marc
14
Paul
14
Donna 17
Vince
13
Zeny
17
Ruby
15
a. If the value of Q1 is 13, describe the ages
of the students.
b. If D7 = 15, how many students have age
15 and below?
c. If 16 years old is the 75th percentile of the
ages of the 15 students, what does it mean?
Arranged Ages
12,12,13,13,14,14,14,14,15,15,15,16,17,17,17
Q1 =15x25% = 15 x 1/4 =15 = 3.75 or 4
4
D7 =15x70% = 15 x 0.70 =10.5 or 11
75% or Q3 =15x75% =11.25
Answer:
a. Since Q1 is 13, then there are 4 students
whose age is less than or equal to 13.
b. Since D7 is 15, then there are 11
students whose age is less than or
equal to 15.
c. It means that 75% of the students are
16 years old and below or 25% of the
students are 16 years old and above.
Directions: Study each problem and
answer what is/are being asked.
1. You are the third tallest student in a
group of 10. If you are the third tallest
student, therefore 7 students are shorter
than you. It also means that 70% of the
students are shorter than you. On the
other hand, if you are the 7th tallest
student in a group of 10, what percent of
the students are shorter than you?
3 students are shorter and also means
Answer: ______________________
that 30% of the students are shorter
than you.
2. Given a test in Statistics, the 75th
percentile score is 20. What does it mean?
What is its measure of position in relation
to the other data?
There are 75% of the test takers
Answer: ______________________
got the scores of 20 and below.
About 25% of the test takers
obtained the scores of above 20.
The measure of position of the
score 20 is in Q3 or in P75
3. The 78th percentile means 78% are
smaller than the given value. Does
making the 80th percentile mean that you
made an 80% on test? Justify.
No. because the 80th percentile
Answer: ______________________
would mean that a person did
better than 80% of the students
who took the test.
Directions: Match Column A with Column B.
A
B
1. Q1
A. Median
2. Q2
B. Median of the lower half
3. Q3
C. Median of the upper half
4. D5
D. D3
5. P30
E. P50
6. D1
F. D4
7. D2
G. P70
8. P40
H. P60
9. D7
I. P10
10.D6
J. P20
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