Download - Mode (Grouped Data)
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Purpose/Rationale of this Module
This module is designed to provide studentswith a step by step discussion on thecomputation 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 visualpresentation of the subject.
Enjoy!
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What Will You Learn From ThisModule?
After studying this module, you shouldbe able to:
1. Compute the mode for groupeddata.
2. Use mode for grouped data toanalyze and interpret data to solveproblems in daily life.
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Let’s See What You Already
Know
Before you start studying this
module, take the following testfirst to find out how prepared you are to solve for the mode of
grouped data.
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Find the mode of each of thefollowing sets of numbers.
a. 2, 4, 5, 1, 4, 6
b. 77, 80, 90, 65, 77, 89, 80
c. 1299, 2580, 4098, 9100, 1100
Answer
Answer
Answer
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Answer: 4
Click meto answer
letter b.
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Answer: 77 and 80
Click meto answerletter c.
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Answer: No Mode
Go Back CONTINUE
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For the next set of questions, refer tothe given frequency distributiontable of the grades of a group of
students.
CONTINUE
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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
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ANSWER: 75 – 79
The modal class is the class with thehighest frequency.
CONTINUE
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2. What is the lower class boundaryof the modal class?
Grades Number of students
90 – 94 2
85 – 89 5
80 – 84 8
(Modal Class) 75 – 79 1270 – 74 3
ANSWER
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ANSWER: Lmo = 74.5
CONTINUE
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3. What is the frequency of themodal class?
Grades Number of students
90 – 94 2
85 – 89 5
80 – 84 8
(Modal Class) 75 – 79 12
70 – 74 3
ANSWER
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ANSWER: f mo = 12
CONTINUE
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4. What is the frequency of the classpreceding the modal class?
Grades Number of students
90 – 94 2
85 – 89 5
80 – 84 8
(Modal Class) 75 – 79 12
70 – 74 3
ANSWER
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ANSWER: f 1 = 8
CONTINUE
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5. What is the frequency of the classafter the modal class?
Grades Number of students
90 – 94 2
85 – 89 5
80 – 84 8
(Modal Class) 75 – 79 12
70 – 74 3
ANSWER
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ANSWER: f 2 = 3
CONTINUE
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ANSWER: i = 5
CONTINUE
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74.5 is the lower
class boundary ofthe modal class
(Lmo)
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12 is the frequency
of the modal class(f mo)
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3 is the frequency of
the class after themodal class (f 2).
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5 is the class size (i).
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T l f th d f d d t
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To solve for the mode of grouped data,use the formula
Mo = Lmo+{( f mo – f 1 )/( 2f mo – f 1 – f 2 )}iwhere,
Lmo is the lower class boundary of the modal
class,f mo is the frequency of the modal class,
f 1 is the frequency of the class preceding the
modal class,f 2 is the frequency of the class after the
modal class, and
i is the class size. CONTINUE
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Let’s Practice!
The followingdistribution gives thenumber of hours
allotted by 50students to do theirassignments in aweek. Find the modal
hour.
Hours Number ofStudents
1 - 4 9
5 - 8 12
9 - 12 14
13 - 16 10
17 - 20 4SOLUTION
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Modal Class :
Lmo :
f mo :
f 1 :
f 2 :
i :
Hours Number ofStudents
1 - 4 9
5 - 8 12
9 - 12 14
13 - 16 10
17 - 20 4
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9 – 12Modal Class :
Lmo :
f mo :
f 1 :
f 2 :
i :
Hours Numberof
Students1 - 4 9
5 - 8 12
9 - 12 14
13 - 16 10
17 - 20 4
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9 – 12
8.5
14
Modal Class :
Lmo :
f mo :
f 1 :
f 2 :
i :
Hours Numberof
Students1 - 4 9
5 - 8 12
9 - 12 14
13 - 16 10
17 - 20 4
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9 – 12
8.5
14
12
Modal Class :
Lmo :
f mo :
f 1 :
f 2 :
i :
Hours Numberof
Students1 - 4 9
5 - 8 12
9 - 12 14
13 - 16 10
17 - 20 4
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9 – 12
8.5
14
12
10
Modal Class :
Lmo :
f mo :
f 1 :
f 2 :
i :
Hours Numberof
Students1 - 4 9
5 - 8 12
9 - 12 14
13 - 16 10
17 - 20 4
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9 – 12
8.5
14
12
10
4
Modal Class :
Lmo :
f mo :
f 1 :
f 2 :
i :
Compute the mode
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More Practice?
Find the mode using thefrequency distributionof the heights of 40
students.
Height(inches) No. ofStudents
52 – 54 2
55 – 57 458 – 60 3
61- 63 8
64 – 66 10
67 – 69 9
70 - 72 4
SKIP
SOLUTION
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Mo = 63.5 + {[10 – 8] / [2(10) – 8 - 9]}3
= 63.5 + (2/3)3
= 63.5 + 2
= 65.5NEXT
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EVALUATE YOURSELF
Find the mode of 20students whosescores on a 15-point
test are given in thefollowing distribution:
Scores No. ofStudents
1 – 3 1
4 – 6 4
7 – 9 8
10 – 12 5
13 - 15 2
SOLUTION
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Mo = 6.5 + {[8 – 4] / [2(8) – 4 - 5]}3
= 6.5 + (4/7)3
= 6.5 + 1.714
= 8.21NEXT