Measures of Central Measures of Central TendencyTendency

MODE (Grouped Data)MODE (Grouped Data)

Prepared by:Prepared by:

Ryan L. Race Jenelyn A. Ryan L. Race Jenelyn A. SamsamanSamsaman

Rafaela M. Sarmiento Jorge O. Dela CruzRafaela M. Sarmiento Jorge O. Dela Cruz

Maria Theresa S. Parajas Luningning B. Maria Theresa S. Parajas Luningning B. FederizoFederizo

Purpose/Rationale of this Purpose/Rationale of this ModuleModule

This module is designed to provide This module is designed to provide students with a step by step students with a step by step discussion on the computation of the discussion on the computation of the mode for grouped data.mode for grouped data.

It is to let the students discover for It is to let the students discover for themselves how to compute for the themselves how to compute for the mode (grouped data) through an mode (grouped data) through an easy visual presentation of the easy visual presentation of the subject.subject.

Enjoy!Enjoy!

What Will You Learn From What Will You Learn From This Module?This Module?

After studying this module, you After studying this module, you should be able to:should be able to:

1.1. Compute the mode for grouped Compute the mode for grouped data.data.

2.2. Use mode for grouped data to Use mode for grouped data to analyze and interpret data to analyze and interpret data to solve problems in daily life.solve problems in daily life.

Let’s See What You Let’s See What You Already KnowAlready Know

Before you start studying Before you start studying this module, take the this module, take the following test first to find out following test first to find out how prepared you are to how prepared you are to solve for the mode of solve for the mode of grouped data.grouped data.

Find the mode of each of the Find the mode of each of the following sets of numbers.following sets of numbers.

aa. . 2, 4, 5, 1, 4, 62, 4, 5, 1, 4, 6

b. b. 77, 80, 90, 65, 77, 89, 8077, 80, 90, 65, 77, 89, 80

c. c. 1299, 2580, 4098, 9100, 11001299, 2580, 4098, 9100, 1100

Answer

Answer

Answer

Answer: 4Answer: 4

Click meto answer letter b.

Answer: 77 and Answer: 77 and 8080

Click meto answerletter c.

Answer: No Answer: No ModeMode

Go Back CONTINUE

For the next set of questions, For the next set of questions, refer to the given frequency refer to the given frequency

distribution table of the grades distribution table of the grades of a group of students.of a group of students.

CONTINUE

1. What is the modal class?1. What is the modal class?

GradesGrades Number of Number of studentsstudents

90 – 9490 – 94 22

85 – 8985 – 89 55

80 – 8480 – 84 88

75 – 7975 – 79 1212

70 – 7470 – 74 33

ANSWER

ANSWER: 75 – 79ANSWER: 75 – 79

The modal class is the class with The modal class is the class with the highest frequency.the highest frequency.

CONTINUE

2. What is the lower class 2. What is the lower class boundary of the modal class?boundary of the modal class?

GradesGrades Number of studentsNumber of students

90 – 9490 – 94 22

85 – 8985 – 89 55

80 – 8480 – 84 88

(Modal Class) (Modal Class) 75 – 75 – 7979

1212

70 – 7470 – 74 33

ANSWER

ANSWER: LANSWER: Lmo mo = = 74.574.5

CONTINUE

3. What is the frequency of 3. What is the frequency of the modal class?the modal class?

GradesGrades Number of Number of studentsstudents

90 – 9490 – 94 22

85 – 8985 – 89 55

80 – 8480 – 84 88

(Modal Class) (Modal Class) 75 – 75 – 7979

1212

70 – 7470 – 74 33ANSWER

ANSWER: fANSWER: fmo mo = 12= 12

CONTINUE

4. What is the frequency of the 4. What is the frequency of the class preceding the modal class?class preceding the modal class?

GradesGrades Number of Number of studentsstudents

90 – 9490 – 94 22

85 – 8985 – 89 55

80 – 8480 – 84 88

(Modal Class)(Modal Class) 75 – 75 – 7979

1212

70 – 7470 – 74 33ANSWER

ANSWER: fANSWER: f11 = 8 = 8

CONTINUE

5. What is the frequency of the 5. What is the frequency of the class after the modal class?class after the modal class?

GradesGrades Number of Number of studentsstudents

90 – 9490 – 94 22

85 – 8985 – 89 55

80 – 8480 – 84 88

(Modal Class) (Modal Class) 75 – 75 – 7979

1212

70 – 7470 – 74 33ANSWER

ANSWER: fANSWER: f2 2 = 3 = 3

CONTINUE

6. What is the class size?6. What is the class size?

GradesGrades Number of Number of studentsstudents

90 – 9490 – 94 22

85 – 8985 – 89 55

80 – 8480 – 84 88

75 – 7975 – 79 1212

70 – 7470 – 74 33

ANSWER

ANSWER: i = 5ANSWER: i = 5

CONTINUE

Observe how the modal grade of Observe how the modal grade of the students is computed. the students is computed.

Mode (Mo) Mode (Mo)

= +{[( – )]/[2( ) – – ]} = +{[( – )]/[2( ) – – ]}

= 74.5 + (4/13)5= 74.5 + (4/13)5

= 74.5 + (20/13)= 74.5 + (20/13)

= 76.04= 76.04

74.5 12 8 12 8 3 5

CONTINUE

74.5 is the lower 74.5 is the lower class boundary of class boundary of the modal class the modal class

(L(Lmomo))

12 is the 12 is the frequency of the frequency of the modal class (fmodal class (fmomo))

8 is the frequency 8 is the frequency of the class of the class

preceding the preceding the modal class (fmodal class (f11))

3 is the frequency 3 is the frequency of the class after of the class after the modal class the modal class

(f(f22).).

5 is the class size 5 is the class size (i).(i).

How did we solve for the How did we solve for the modal grade of the modal grade of the

students?students?

Can you give the formula Can you give the formula for the mode of grouped for the mode of grouped

data?data?CONTINUE

To solve for the mode of grouped To solve for the mode of grouped data, use the formuladata, use the formula

Mo = Lmo+{( fmo – f1 )/( 2fmo – f1 – f2 )}i

where,where,

LLmomo is the lower class boundary of the is the lower class boundary of the modal class,modal class,

ffmomo is the frequency of the modal class, is the frequency of the modal class,

ff11 is the frequency of the class is the frequency of the class preceding the modal class,preceding the modal class,

ff22 is the frequency of the class after is the frequency of the class after the modal class, andthe modal class, and

i i is the class size.is the class size. CONTINUE

Let’s Practice!Let’s Practice!

The following The following distribution gives distribution gives the number of the number of hours allotted by hours allotted by 50 students to do 50 students to do their assignments their assignments in a week. Find the in a week. Find the modal hour.modal hour.

HoursHours Number Number of of

StudentsStudents

1 - 41 - 4 99

5 - 85 - 8 1212

9 - 129 - 12 1414

13 - 1613 - 16 1010

17 - 2017 - 20 44SOLUTION

Modal Class :

Lmo :

fmo :

f1 :

f2 :

i :

HoursHours Number Number of of

StudentsStudents

1 - 41 - 4 99

5 - 85 - 8 1212

9 - 129 - 12 1414

13 - 1613 - 16 1010

17 - 2017 - 20 44

9 – 9 – 1212

Modal Class :

Lmo :

fmo :

f1 :

f2 :

i :

HoursHours NumbeNumber of r of

StudentStudentss

1 - 41 - 4 99

5 - 85 - 8 1212

9 - 129 - 12 1414

13 - 1613 - 16 1010

17 - 2017 - 20 44

9 – 9 – 1212

8.58.5

Modal Class :

Lmo :

fmo :

f1 :

f2 :

i :

HoursHours NumbeNumber of r of

StudenStudentsts

1 - 41 - 4 99

5 - 85 - 8 1212

9 - 129 - 12 1414

13 - 1613 - 16 1010

17 - 2017 - 20 44

9 – 9 – 1212

8.58.5

1414

Modal Class :

Lmo :

fmo :

f1 :

f2 :

i :

HoursHours Number Number of of

StudentStudentss

1 - 41 - 4 99

5 - 85 - 8 1212

9 - 129 - 12 1414

13 - 1613 - 16 1010

17 - 2017 - 20 44

9 – 9 – 1212

8.58.5

1414

1212

Modal Class :

Lmo :

fmo :

f1 :

f2 :

i :

HoursHours Number Number of of

StudentStudentss

1 - 41 - 4 99

5 - 85 - 8 1212

9 - 129 - 12 1414

13 - 1613 - 16 1010

17 - 2017 - 20 44

9 – 9 – 1212

8.58.5

1414

1212

1010

Modal Class :

Lmo :

fmo :

f1 :

f2 :

i :

HoursHours Number Number of of

StudentStudentss

1 - 41 - 4 99

5 - 85 - 8 1212

9 - 129 - 12 1414

13 - 1613 - 16 1010

17 - 2017 - 20 44

9 – 129 – 12

8.58.5

1414

1212

1010

44

Modal Class :

Lmo :

fmo :

f1 :

f2 :

i :

Compute the mode

Mo = 8.5 + {[14 – 12] / [2(14) – 12 -Mo = 8.5 + {[14 – 12] / [2(14) – 12 -10]}410]}4

= 8.5 + (2/6)4= 8.5 + (2/6)4

= 8.5 + 1.33= 8.5 + 1.33

= = 9.839.83 CONTINUE

More Practice?More Practice?

Find the mode using Find the mode using the frequency the frequency distribution of the distribution of the heights of 40 heights of 40 students.students.

Height(inches)Height(inches) No. of No. of StudentStudent

ss

52 – 5452 – 54 22

55 – 5755 – 57 44

58 – 6058 – 60 33

61- 6361- 63 88

64 – 6664 – 66 1010

67 – 6967 – 69 99

70 - 7270 - 72 44

SKIP

SOLUTION

Mo = 63.5 + {[10 – 8] / [2(10) – 8 - 9]}3Mo = 63.5 + {[10 – 8] / [2(10) – 8 - 9]}3

= 63.5 + (2/3)3= 63.5 + (2/3)3

= 63.5 + 2= 63.5 + 2

= 65.5= 65.5 NEXT

EVALUATE YOURSELFEVALUATE YOURSELF

Find the mode of 20 Find the mode of 20 students whose students whose scores on a 15-scores on a 15-point test are given point test are given in the following in the following distribution:distribution:

ScoresScores No. of No. of StudentsStudents

1 – 31 – 3 11

4 – 64 – 6 44

7 – 97 – 9 88

10 – 1210 – 12 55

13 - 1513 - 15 22

SOLUTION

Mo = 6.5 + {[8 – 4] / [2(8) – 4 - 5]}3Mo = 6.5 + {[8 – 4] / [2(8) – 4 - 5]}3

= 6.5 + (4/7)3= 6.5 + (4/7)3

= 6.5 + 1.714= 6.5 + 1.714

= 8.21= 8.21NEXT

Try Another OneTry Another One

A sample of 40 A sample of 40 tourists traveled to tourists traveled to Puerto Galera with Puerto Galera with the distribution the distribution based on the based on the length of their stay length of their stay (in years). Find the (in years). Find the mode.mode.

Length of Length of Stay Stay

(years)(years)

No. of No. of TouristsTourists

1 – 81 – 8 88

9 – 169 – 16 77

17 – 2417 – 24 55

25 – 3225 – 32 66

33 - 4033 - 40 55

SOLUTION

Mo = 0.5 + {[8 – 0] / [2(8) – 0 - 7]}8Mo = 0.5 + {[8 – 0] / [2(8) – 0 - 7]}8

= 0.5 + (8/9)8= 0.5 + (8/9)8

= 0.5 + 7.1= 0.5 + 7.1

= 7.1= 7.1