Download 9 – 12

Measures of Central Tendency
MODE (Grouped Data)
Prepared by:
Ryan L. Race
Jenelyn A. Samsaman
Rafaela M. Sarmiento
Jorge O. Dela Cruz
Maria Theresa S. Parajas Luningning B. Federizo
Purpose/Rationale of this Module
This module is designed to provide students
with a step by step discussion on the
computation of the mode for grouped
data.
It is to let the students discover for
themselves how to compute for the mode
(grouped data) through an easy visual
presentation of the subject.
Enjoy!
What Will You Learn From This
Module?
After studying this module, you should
be able to:
1. Compute the mode for grouped
data.
2.
Use mode for grouped data to
analyze and interpret data to solve
problems in daily life.
Let’s See What You Already
Know
 Before
you start studying this
module, take the following test
first to find out how prepared
you are to solve for the mode of
grouped data.
Find the mode of each of the
following sets of numbers.
a. 2, 4, 5, 1, 4, 6
Answer
b. 77, 80, 90, 65, 77, 89, 80
Answer
c. 1299, 2580, 4098, 9100, 1100
Answer
Answer: 4
Click me
to answer
letter b.
Answer: 77 and 80
Click me
to answer
letter c.
Answer: No Mode
Go Back
CONTINUE
For the next set of questions, refer to
the given frequency distribution
table of the grades of a group of
students.
CONTINUE
1. What is the modal class?
Grades
Number of students
90 – 94
2
85 – 89
5
80 – 84
8
75 – 79
12
70 – 74
3
ANSWER
ANSWER: 75 – 79
The modal class is the class with the
highest frequency.
CONTINUE
2. What is the lower class boundary
of the modal class?
Grades
90 – 94
Number of students
2
85 – 89
5
80 – 84
8
(Modal Class) 75 – 79
70 – 74
ANSWER
12
3
ANSWER: Lmo = 74.5
CONTINUE
3. What is the frequency of the
modal class?
Grades
90 – 94
85 – 89
80 – 84
(Modal Class) 75 – 79
70 – 74
Number of students
2
5
8
12
3
ANSWER
ANSWER: fmo = 12
CONTINUE
4. What is the frequency of the class
preceding the modal class?
Grades
90 – 94
85 – 89
80 – 84
(Modal Class) 75 – 79
70 – 74
Number of students
2
5
8
12
3
ANSWER
ANSWER: f1 = 8
CONTINUE
5. What is the frequency of the class
after the modal class?
Grades
90 – 94
85 – 89
80 – 84
(Modal Class) 75 – 79
70 – 74
Number of students
2
5
8
12
3
ANSWER
ANSWER: f2 = 3
CONTINUE
6. What is the class size?
Grades
90 – 94
85 – 89
80 – 84
75 – 79
70 – 74
Number of students
2
5
8
12
3
ANSWER
ANSWER: i = 5
CONTINUE
Observe how the modal grade of the
students is computed.
Mode (Mo)
= 74.5 +{[( 12 –
= 74.5 + (4/13)5
8
)]/[2(
12
)–
= 74.5 + (20/13)
= 76.04
CONTINUE
8
–
3
]}
5
74.5 is the lower
class boundary of
the modal class
(Lmo)
12 is the frequency
of the modal class
(fmo)
8 is the frequency of
the class preceding
the modal class (f1)
3 is the frequency of
the class after the
modal class (f2).
5 is the class size (i).
How did we solve for the
modal grade of the students?
Can you give the formula for
the mode of grouped data?
CONTINUE
To solve for the mode of grouped data,
use the formula
Mo = Lmo+{( fmo – f1 )/( 2fmo – f1 – f2 )}i
where,
Lmo is the lower class boundary of the modal
class,
fmo is the frequency of the modal class,
f1 is the frequency of the class preceding the
modal class,
f2 is the frequency of the class after the
modal class, and
i is the class size.
CONTINUE
Let’s Practice!
The following
distribution gives the
number of hours
allotted by 50
students to do their
assignments in a
week. Find the modal
hour.
SOLUTION
Hours
1-4
Number of
Students
9
5-8
12
9 - 12
14
13 - 16
10
17 - 20
4
Modal Class :
Lmo :
fmo :
f1 :
f2 :
i:
Hours
1-4
Number of
Students
9
5-8
12
9 - 12
14
13 - 16
10
17 - 20
4
Modal Class :
9 – 12
Hours
Number
of
Students
1-4
9
5-8
12
9 - 12
14
13 - 16
10
17 - 20
4
Lmo :
fmo :
f1 :
f2 :
i:
Modal Class :
Lmo :
fmo :
f1 :
f2 :
i:
9 – 12
Hours
Number
of
Students
1-4
9
5-8
12
9 - 12
14
13 - 16
10
17 - 20
4
8.5
Modal Class :
Lmo :
fmo :
f1 :
f2 :
i:
9 – 12
Hours
Number
of
Students
1-4
9
5-8
12
9 - 12
14
13 - 16
10
17 - 20
4
8.5
14
Modal Class :
Lmo :
fmo :
f1 :
f2 :
i:
9 – 12
Hours
Number
of
Students
1-4
9
5-8
12
9 - 12
14
13 - 16
10
17 - 20
4
8.5
14
12
Modal Class :
Lmo :
fmo :
9 – 12
Number
of
Students
1-4
9
5-8
12
9 - 12
14
13 - 16
10
17 - 20
4
8.5
14
f1 :
12
f2 :
10
i:
Hours
Modal Class :
9 – 12
Lmo :
8.5
fmo :
14
f1 :
12
f2 :
10
i:
4
Compute the mode
Mo = 8.5 + {[14 – 12] / [2(14) – 12 -10]}4
= 8.5 + (2/6)4
= 8.5 + 1.33
= 9.83
CONTINUE
More Practice?
Find the mode using the
frequency distribution
of the heights of 40
students.
SOLUTION
SKIP
Height(inches)
No. of
Students
52 – 54
2
55 – 57
4
58 – 60
3
61- 63
8
64 – 66
10
67 – 69
9
70 - 72
4
Mo = 63.5 + {[10 – 8] / [2(10) – 8 - 9]}3
= 63.5 + (2/3)3
= 63.5 + 2
= 65.5
NEXT
EVALUATE YOURSELF
Find the mode of 20
students whose
scores on a 15-point
test are given in the
following distribution:
SOLUTION
Scores
1–3
No. of
Students
1
4–6
4
7–9
8
10 – 12
5
13 - 15
2
Mo = 6.5 + {[8 – 4] / [2(8) – 4 - 5]}3
= 6.5 + (4/7)3
= 6.5 + 1.714
= 8.21
NEXT
Try Another One
A sample of 40 tourists
traveled to Puerto
Galera with the
distribution based on
the length of their
stay (in years). Find
the mode.
SOLUTION
Length of
Stay
(years)
1–8
No. of
Tourists
9 – 16
7
17 – 24
5
25 – 32
6
33 - 40
5
8
Mo = 0.5 + {[8 – 0] / [2(8) – 0 - 7]}8
= 0.5 + (8/9)8
= 0.5 + 7.1
= 7.1