Name:
Grade & Section:
Score:
School:
Teacher:
Subject: Math 10
LAS Writer: CARLITO B. DIONEDAS, JR.
Content Editor: EMETERIO J. FLORESCA, JR.
Lesson Topic:
Interpreting measures of position: Quartiles, Deciles and Percentiles. (Quarter 4 Wk. 3 LAS 1)
Learning Targets: Calculate measures of position (grouped data). (M10SP-IVc-1.1)
Reference(s): Callanta, Melvin M. et. al, 2015. Mathematics Grade 10 Learner’s Module. 1st ed. Pasig City: REX
Book Store Inc., pp.383-387.
CONTENT
Recall that the steps in getting the median as similar to that of Q 1 and Q3. In finding the median, we first need to
determine the median class. In the same manner, the Q 1 and Q3 class must be determined first before computing the value
of the Q1 and Q3. The Q1 class is the class interval where the
the
3𝑁
𝑡ℎ
4
𝑁
𝑡ℎ
4
score is contained, while the class interval that contains
score is the Q3 class. In computing the quartiles of grouped data, the following formula is used:
𝑘𝑁
− 𝑐𝑓𝑏
𝑄𝑘 = 𝐿𝐵 + ( 4
)𝑖
𝑓𝑄𝑘
Where: LB = lower boundary of the Qk class
N = total frequency
cfb = cumulative frequency of the class before the Q k class
𝑓𝑄𝑘 = frequency of the Qk class
i = size of the class interval
k = nth quartile, where n = 1, 2, or 3
EXAMPLE:
Find the value of Q1, Q2, and Q3 of the Mathematics test scores of 40 students.
SOLUTION
Scores
Frequency
Scores
Frequency
46 – 50
41 – 45
36 – 40
31 – 35
26 – 30
21 – 25
3
7
9
7
10
4
46 – 50
41 – 45
36 – 40
31 – 35
26 – 30
21 – 25
3
7
9
7
10
4
N= 40
Q1 class:
𝑁
4
=
40
4
= 10
This means we need to find the class
interval where the 10th score is contained.
Note that the 5th – 14th scores belong to
the class interval: 26 – 30.
So the 10th score is also within the class
interval 26 – 30.
Q2 class:
2𝑁
4
=
2(40)
4
=
80
4
= 20
This means we need to find the class
interval where the 20th score is contained.
Note that the 15th – 21st scores belong to
the class interval: 31 – 35.
So the 20th score is also within the class
interval 31 – 35.
Lower
Boundaries
(LB)
45.5
40.5
35.5
30.5
25.5
20.5
Less than
Cumulative
Frequency (<cf)
40
37
30
21
14
4
LB = 25.5
N = 40
cfb = 4
𝑓𝑄1 = 10
i=5
𝑘𝑁
− 𝑐𝑓𝑏
𝑄𝑘 = 𝐿𝐵 + ( 4
)𝑖
𝑓𝑄𝑘
LB = 30.5
N = 40
cfb = 10
𝑓𝑄2 = 7
i=5
𝑘𝑁
− 𝑐𝑓𝑏
𝑄𝑘 = 𝐿𝐵 + ( 4
)𝑖
𝑓𝑄𝑘
10 − 4
)5
10
6
𝑄1 = 25.5 + ( ) 5
10
𝑄1 = 25.5 + 3
Q1 = 28.5
Therefore, 25% of the students have
score less than 28.5.
𝑄1 = 25.5 + (
20 − 10
)5
7
10
𝑄1 = 30.5 + ( ) 5
10
𝑄1 = 30.5 + 5
Q1 = 35.5
Therefore, 50% of the students have
score less than or equal to 35.5.
𝑄1 = 30.5 + (
Q3 class:
3𝑁
4
=
3(40)
4
=
120
4
= 30
This means we need to find the class
interval where the 20th score is contained.
Note that the 15th – 21st scores belong to
the class interval: 31 – 35.
So the 20th score is also within the class
interval 31 – 35.
LB = 35.5
N = 40
cfb = 7
𝑓𝑄2 = 9
i=5
𝑘𝑁
− 𝑐𝑓𝑏
𝑄𝑘 = 𝐿𝐵 + ( 4
)𝑖
𝑓𝑄𝑘
30 − 7
)5
9
23
𝑄1 = 35.5 + ( ) 5
9
𝑄1 = 35.5 + 12.78
Q1 = 48.28
Therefore, 75% of the students have
score less than or equal to 48.28.
𝑄1 = 35.5 + (
ACTIVITY
The following is a distribution for the number of employees in 45 companies belonging to a certain industry.
Calculate the Q1, Q2 and Q3 of the number of employees given the number of companies.
Number of employees Number of companies
41 – 45
11
36 – 40
6
31 – 35
9
26 – 30
7
21 – 25
8
16 – 20
4