This document discusses measures of central tendency, specifically how to calculate the mean of grouped data. It provides the formula for calculating the mean of grouped data and walks through an example of finding the mean test scores of students. The document demonstrates how to find the midpoint of each score group, multiply by the frequency, sum the results, and divide by the total frequency to determine the mean.

1. 1

2. Measures of Central Tendency
2

3. 3
Determine the mean of
the following.

4. 4

5. 5

6. 6

7. 7

8. 8

9. 9

10. 10

11. 11

12. 12

13. 13

14. 14
Measures of Central Tendency of
GROUPED DATA

15. 15
Grouped Data

16. Grouped data are the data or scores
that are arranged in a frequency
distribution.
16
Grouped Data

17. 17
Mean

18. The mean (also known as the
arithmetic mean) is the most
commonly used measure of central
position. It is used to describe a set of
data where the measures cluster or
concentrate at a point.18
Mean

19. Formula:
19
mfX
X
n



20. f frequency
mX classmark
n sum of frequency
20
X mean
mfX
X
n

Where:

21. 21
Illustrative Example:
Calculate the mean of the Mid-year Scores of
Students in Mathematics.
Score Frequency
41-45 1
36-40 8
31-35 8
26-30 14
21-25 7
16-20 2
Mid-year Test scores of students in Mathematics

22. 22
Solution
1. Find the midpoint or class mark ( ) of each
class or category.
mX
2
m
LL UL
X


Scores
41-45 1
36-40 8
31-35 8
26-30 14
21-25 7
16-20 2

23. 23
Solution
1. Find the midpoint or class mark ( ) of each
class or category.
mX
2
m
LL UL
X


Scores
41-45 1 43
36-40 8
31-35 8
26-30 14
21-25 7
16-20 2

24. 24
Solution
1. Find the midpoint or class mark ( ) of each
class or category.
mX
2
m
LL UL
X


Scores
41-45 1 43
36-40 8 38
31-35 8
26-30 14
21-25 7
16-20 2

25. 25
Solution
1. Find the midpoint or class mark ( ) of each
class or category.
mX
2
m
LL UL
X


Scores
41-45 1 43
36-40 8 38
31-35 8 33
26-30 14
21-25 7
16-20 2

26. 26
Solution
1. Find the midpoint or class mark ( ) of each
class or category.
mX
2
m
LL UL
X


Scores
41-45 1 43
36-40 8 38
31-35 8 33
26-30 14 28
21-25 7
16-20 2

27. 27
Solution
1. Find the midpoint or class mark ( ) of each
class or category.
mX
2
m
LL UL
X


Scores
41-45 1 43
36-40 8 38
31-35 8 33
26-30 14 28
21-25 7 23
16-20 2

28. 28
Solution
1. Find the midpoint or class mark ( ) of each
class or category.
mX
2
m
LL UL
X


Scores
41-45 1 43
36-40 8 38
31-35 8 33
26-30 14 28
21-25 7 23
16-20 2 18

29. 29
Solution
2. Multiply the frequency and the corresponding
class mark . fXm
Scores Frequency
(f )
41-45 1 43
36-40 8 38
31-35 8 33
26-30 14 28
21-25 7 23
16-20 2 18

30. 30
Solution
2. Multiply the frequency and the corresponding
class mark . fXm
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38
31-35 8 33
26-30 14 28
21-25 7 23
16-20 2 18

31. 31
Solution
2. Multiply the frequency and the corresponding
class mark . fXm
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38 304
31-35 8 33
26-30 14 28
21-25 7 23
16-20 2 18

32. 32
Solution
2. Multiply the frequency and the corresponding
class mark . fXm
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38 304
31-35 8 33 264
26-30 14 28
21-25 7 23
16-20 2 18

33. 33
Solution
2. Multiply the frequency and the corresponding
class mark . fXm
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38 304
31-35 8 33 264
26-30 14 28 392
21-25 7 23
16-20 2 18

34. 34
Solution
2. Multiply the frequency and the corresponding
class mark . fXm
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38 304
31-35 8 33 264
26-30 14 28 392
21-25 7 23 161
16-20 2 18

35. 35
Solution
2. Multiply the frequency and the corresponding
class mark . fXm
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38 304
31-35 8 33 264
26-30 14 28 392
21-25 7 23 161
16-20 2 18 36

36. 36
Solution
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38 304
31-35 8 33 264
26-30 14 28 392
21-25 7 23 161
16-20 2 18 36
3. Find the sum of the results in step 2. fXm

37. 37
Solution
3. Find the sum of the results in step 2.
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38 304
31-35 8 33 264
26-30 14 28 392
21-25 7 23 161
16-20 2 18 36
fXm

38. Solution
4. Solve the mean using the formula.
Scores Frequency
(f )
41-45 1 43 43
36-40 8 38 304
31-35 8 33 264
26-30 14 28 392
21-25 7 23 161
16-20 2 18 36
n=40
Substitution
Therefore, the
mean of Mid-
year test is 30.
mfX
X
n


1,200
40

30X 

39. 39
Let’s practice: Find the mean weight of
Grade 8 Students.
Weight in kg Frequency
75-79 1
70-74 4
65-69 10
60-64 14
55-59 21
50-54 15
45-49 14
40-44 1

40. Weight in kg Frequency (f)
75-79 1
70-74 4
65-69 10
60-64 14
55-59 21
50-54 15
45-49 14
40-44 1
40

41. Weight in kg Frequency (f)
75-79 1 77
70-74 4
65-69 10
60-64 14
55-59 21
50-54 15
45-49 14
40-44 1
41

42. Weight in kg Frequency (f)
75-79 1 77
70-74 4 72
65-69 10
60-64 14
55-59 21
50-54 15
45-49 14
40-44 1
42

43. Weight in kg Frequency (f)
75-79 1 77
70-74 4 72
65-69 10 67
60-64 14
55-59 21
50-54 15
45-49 14
40-44 1
43

44. Weight in kg Frequency (f)
75-79 1 77
70-74 4 72
65-69 10 67
60-64 14 62
55-59 21
50-54 15
45-49 14
40-44 1
44

45. Weight in kg Frequency (f)
75-79 1 77
70-74 4 72
65-69 10 67
60-64 14 62
55-59 21 57
50-54 15
45-49 14
40-44 1
45

46. Weight in kg Frequency (f)
75-79 1 77
70-74 4 72
65-69 10 67
60-64 14 62
55-59 21 57
50-54 15 52
45-49 14
40-44 1
46

47. Weight in kg Frequency (f)
75-79 1 77
70-74 4 72
65-69 10 67
60-64 14 62
55-59 21 57
50-54 15 52
45-49 14 47
40-44 1
47

48. Weight in kg Frequency (f)
75-79 1 77
70-74 4 72
65-69 10 67
60-64 14 62
55-59 21 57
50-54 15 52
45-49 14 47
40-44 1 42
48

49. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72
65-69 10 67
60-64 14 62
55-59 21 57
50-54 15 52
45-49 14 47
40-44 1 42
49

50. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67
60-64 14 62
55-59 21 57
50-54 15 52
45-49 14 47
40-44 1 42
50

51. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67 670
60-64 14 62
55-59 21 57
50-54 15 52
45-49 14 47
40-44 1 42
51

52. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67 670
60-64 14 62 868
55-59 21 57
50-54 15 52
45-49 14 47
40-44 1 42
52

53. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67 670
60-64 14 62 868
55-59 21 57 1197
50-54 15 52
45-49 14 47
40-44 1 42
53

54. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67 670
60-64 14 62 868
55-59 21 57 1197
50-54 15 52 780
45-49 14 47
40-44 1 42
54

55. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67 670
60-64 14 62 868
55-59 21 57 1197
50-54 15 52 780
45-49 14 47 658
40-44 1 42
55

56. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67 670
60-64 14 62 868
55-59 21 57 1197
50-54 15 52 780
45-49 14 47 658
40-44 1 42 42
56

57. Weight in kg Frequency (f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67 670
60-64 14 62 868
55-59 21 57 1197
50-54 15 52 780
45-49 14 47 658
40-44 1 42 42
57

58. Therefore, the
mean weight is
57.25
Weight in
kg
Frequency
(f)
75-79 1 77 77
70-74 4 72 288
65-69 10 67 670
60-64 14 62 868
55-59 21 57 1197
50-54 15 52 780
45-49 14 47 658
40-44 1 42 42
mfX
X
n


4580
80

57.25X 

59. 59
Generalization

60. 60
Generalization
The mean (also known as the
arithmetic mean) is the most
commonly used measure of central
position. It is used to describe a set
of data where the measures cluster
or concentrate at a point.

61. 61
Formula
mfX
X
n



62. 62
Group Work
CRITERIA
5 4 3 2 1

63. 63
Group Work
CRITERIA
5 4 3 2 1
ACCURACY 100% of the steps
and solutions
have no
mathematical
errors.
Almost all (90-
99%) of the steps
and solutions
have no
mathematical
errors.
Almost all (85-
89%) of the steps
and solutions
have no
mathematical
errors.
Most (75-84%) of
the steps and
solutions have
no mathematical
errors.
Less than 75% of
the steps and
solutions have
mathematical
errors.

64. 64
Group Work
CRITERIA
5 4 3 2 1
ORGANIZATION It uses an
appropriate and
complete strategy
for solving the
problem. Uses clear
and effective
diagrams and/or
tables.
It uses complete
strategy for solving
the problem. Uses
creative diagrams
and/or tables.
It uses strategy for
solving the
problem. Uses
diagrams and/or
tables.
It uses an
inappropriate
strategy or
application of
strategy unclear.
There is limited
use or misuse of
diagrams and/or
tables.
It has no particular
strategy for
solving the
problem. It does
not show use of
diagrams nor
tables.

65. 65
Group Work
CRITERIA
5 4 3 2 1
DELIVERY There is a clear and
effective explanation
of the solution. All
steps are included so
the audience does
not have to infer how
the task was
completed.
Mathematical
representation is
actively used as a
means of
communicating ideas,
and precise and
appropriate
mathematical
terminology.
There is a clear
explanation and
appropriate use of
accurate
mathematical
representation. There
is effective use of
mathematical
terminology.
There is explanation
and mathematical
representation.
There is
mathematical
terminology
There is an
incomplete
explanation; it is not
clearly represented.
There is some use of
appropriate
mathematical
representation and
terminology to the
task.
There is no
explanation of the
solutions. The
explanation cannot
be understood, or is
unrelated to the
task. There is no use
or inappropriate use
of mathematical
representation and
terminology to the
task.

66. TIMER
10 minutes
End

67. 67
Assignment
1. A telecommunications company is conducting a study on the
average number text messages send per day by high school
students in Marikina. A random sample of 50 college students
from the said area is taken. Find the mean of the data set.
Class Interval Frequency
30-34 8
25-29 10
20-24 16
15-19 9
10-14 7

68. 68
2. Study on Median for Grouped Data
a.Describe Median.
b.What is the formula in computing the
median for grouped data?
Reference: Mathematics Learner’s Module by
Emmanuel P. Abunzo
Pages 564-580

69. 69