This document discusses the concept of mode in grouped data. It provides examples of calculating the mode of different data sets. The mode is the value that occurs most frequently in a data set. For grouped data, the mode is calculated using a formula that considers the lower boundary of the modal class, the frequency of the modal class, and the frequencies of neighboring classes. Worked examples demonstrate applying this formula to frequency distributions to determine the modal value.

1. Mathematics 7
M e a s u r e s o f C e n t r a l T e n d e n c y
MODE of Grouped Data
MR. CARLO JUSTINO J. LUNA
Malabanias Integrated School
Angeles City

2. The only way to learn
mathematics
is to do
mathematics.

3. Activity: What-You-Already-Know
Find the mode of each of the following sets of
numbers.
a. 3, 2, 2, 4, 5, 1, 4, 6, 4
b. 77, 80, 90, 65, 77, 89, 80
c. 1987, 1993, 1985, 1990
Answer
Answer
Answer

4. a. 3, 2, 2, 4, 5, 1, 4, 6, 4
MODE: 4

5. b. 77, 80, 90, 65, 77, 89, 80
MODE: 77 and 80

6. c. 1987, 1993, 1985, 1990
MODE: No mode

7. For the next set of questions,
refer to the given frequency
distribution table of the
grades of a group of students.

8. 1. Determine the modal class.
Grades
Number of
Students
91 – 95 3
86 – 90 7
81 – 85 18
76 – 80 12
71 – 75 5
Answer

9. Modal Class: 81 – 85
The modal class is the class with the
highest frequency.

10. 2. What is the lower class boundary of the
modal class?
Grades
Number of
Students
91 – 95 3
86 – 90 7
81 – 85 18
76 – 80 12
71 – 75 5 Answer
Modal Class

11. lbmo = 80.5

12. 3. What is the frequency of the modal
class?
Grades
Number of
Students
91 – 95 3
86 – 90 7
81 – 85 18
76 – 80 12
71 – 75 5 Answer
Modal Class

13. fmo = 18

14. 4. What is the frequency of the class
preceding the modal class?
Grades
Number of
Students
91 – 95 3
86 – 90 7
81 – 85 18
76 – 80 12
71 – 75 5 Answer
Modal Class

15. fb = 12

16. 5. What is the frequency of the class after
the modal class?
Grades
Number of
Students
91 – 95 3
86 – 90 7
81 – 85 18
76 – 80 12
71 – 75 5 Answer
Modal Class

17. fa = 7

18. 6. What is the class size?
Answer
Grades
Number of
Students
91 – 95 3
86 – 90 7
81 – 85 18
76 – 80 12
71 – 75 5

19. i = 5

20. Solution
Observe how the modal grade of the students is computed.
Mo = +80.5
[ 18 –___________________
2( ) – –
12
5
18 12 7
]
= 80.5 +
6
17
5
= 80.5 + 0.35 5
= 80.5 + 1.75
= 𝟖𝟐. 𝟐𝟓
Hence, the modal grade
of the students is 82.25.

21. 80.5 is the lower
class boundary of the
modal class
lbmo

22. 18 is the frequency
of the modal class
fmo

23. 12 is the frequency
of the class before
the modal class
fb

24. 7 is the frequency of
the class after the
modal class
fa

25. 5 is the class size
i

26. How did we solve for the
modal grade of the students?
Can you give the formula for
the mode of grouped data?

27. Formula
To solve for the mode of grouped data, use the formula:
𝑀𝑜 = 𝑙𝑏 𝑚𝑜 +
𝑓𝑚𝑜 − 𝑓𝑏
2 𝑓𝑚𝑜 − 𝑓𝑏 − 𝑓𝑎
𝑖
where
𝑙𝑏 𝑚𝑜 is the lower class boundary of the modal class
𝑓𝑚𝑜 is the frequency of the modal class
𝑓𝑏 is the frequency of the class before the modal class
𝑓𝑎 is the frequency of the class after the modal class
𝑖 is the class size

28. 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.
Hours
Number of
Students
17 – 20 4
13 – 16 10
9 – 12 14
5 – 8 12
1 – 4 9

29. SOLUTION
Hours
Number of
Students
17 – 20 4
13 – 16 10
9 – 12 14
5 – 8 12
1 – 4 9
Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:

30. Hours
Number of
Students
17 – 20 4
13 – 16 10
9 – 12 14
5 – 8 12
1 – 4 9
Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
9 – 12
SOLUTION

31. Hours
Number of
Students
17 – 20 4
13 – 16 10
9 – 12 14
5 – 8 12
1 – 4 9
Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
9 – 12
8.5
SOLUTION

32. Hours
Number of
Students
17 – 20 4
13 – 16 10
9 – 12 14
5 – 8 12
1 – 4 9
Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
9 – 12
8.5
14
SOLUTION

33. Hours
Number of
Students
17 – 20 4
13 – 16 10
9 – 12 14
5 – 8 12
1 – 4 9
Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
9 – 12
8.5
14
12
SOLUTION

34. Hours
Number of
Students
17 – 20 4
13 – 16 10
9 – 12 14
5 – 8 12
1 – 4 9
Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
9 – 12
8.5
14
12
10
SOLUTION

35. Hours
Number of
Students
17 – 20 4
13 – 16 10
9 – 12 14
5 – 8 12
1 – 4 9
Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
9 – 12
8.5
14
12
10
4 Compute the mode.
SOLUTION

36. Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
9 – 12
8.5
14
12
10
4
SOLUTION
= 8.5 +
2
6
4
𝑀𝑜 = 𝑙𝑏 𝑚𝑜 +
𝑓𝑚𝑜 − 𝑓𝑏
2 𝑓𝑚𝑜 − 𝑓𝑏 − 𝑓𝑎
𝑖
= 8.5 +
14 − 12
2 14 − 12 − 10
4
𝑴𝒐 = 𝟗. 𝟖𝟐
= 8.5 + (0.33)4
= 8.5 + 1.32

37. MORE PRACTICE!
Find the mode
using the
frequency
distribution of the
heights of 40
students.
Height
(inches)
Number of
Students
70 – 72 4
67 – 69 9
64 – 66 10
61 – 63 8
58 – 60 3
55 – 57 4
52 – 54 2SOLUTION
SKIP

38. Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
64 – 66
63.5
10
8
9
3
SOLUTION
= 63.5 +
2
3
3
𝑀𝑜 = 𝑙𝑏 𝑚𝑜 +
𝑓𝑚𝑜 − 𝑓𝑏
2 𝑓𝑚𝑜 − 𝑓𝑏 − 𝑓𝑎
𝑖
= 63.5 +
10 − 8
2 10 − 8 − 9
3
𝑴𝒐 = 𝟔𝟓. 𝟓
= 63.5 + 2

39. EVALUATE YOURSELF
Find the mode of
20 students
whose scores on a
15-point test are
given in the
following
distribution:
Scores
Number of
Students
13 – 15 2
10 – 12 5
7 – 9 8
4 – 6 4
1 – 3 1
SOLUTION

40. Modal Class :
𝒍𝒃 𝒎𝒐:
𝒇 𝒎𝒐:
𝒇 𝒃:
𝒇 𝒂:
𝒊:
7 – 9
6.5
8
4
5
3
SOLUTION
= 6.5 +
4
7
3
𝑀𝑜 = 𝑙𝑏 𝑚𝑜 +
𝑓𝑚𝑜 − 𝑓𝑏
2 𝑓𝑚𝑜 − 𝑓𝑏 − 𝑓𝑎
𝑖
= 6.5 +
8 − 4
2 8 − 4 − 5
3
𝑴𝒐 = 𝟖. 𝟐𝟏
= 6.5 + 0.57 3
= 6.5 + 1.71

41. VALUING:
Do you have a person or a
thing in your life that you
consider as a mode?

42. Mathematics 7
M e a s u r e s o f C e n t r a l T e n d e n c y
MODE of Grouped Data
MR. CARLO JUSTINO J. LUNA
Malabanias Integrated School
Angeles City