Lecture on Measures of Central Tendency for Grade 7 Students under the K to 12 Curriculum (Philippines)

1. Measures of Central
Tendency
(Ungrouped Data)
REYNALDO D. SALAYOG, II-LPT-MEd Math

6. TRY THIS!
The grades in Chemistry of 10 students
are 87, 84, 85, 85, 86, 90, 79, 82, 78, 76. What is
the MEAN grade of the 10 students?

9. =
3 1.75 + 3 2.0 + 5 1.75 + 3 1.5 + 3 1.5 + 2(1.0)
3 + 3 + 5 + 3 + 3 + 2

11. Median for Odd Sample:
The median is the middle number when the data
are arranged in order.
Median for Even Sample:
When there are even samples , the median is the
mean of the two middle numbers.
𝑀𝑑 =
𝑛 + 1
2
FORMULA:
Where:
n=number of cases
Md=location of the median

16. TRY THIS!
SOLUTION:
1. No mode
2. VS
3. 3.5 and 4.0
4. 117

19. GRADED ASSESSMENT:

20. Measures of Central
Tendency
(Grouped Data)
REYNALDO D. SALAYOG, II-LPT-MEd Math

21. MEAN of Grouped Data:
Grouped data are the data or scores that
are arranged in a frequency distribution.
One formula in solving the mean for grouped
data is called midpoint method.
The formula is: 𝑥 =
𝑓𝑥 𝑚
𝑓
𝑤ℎ𝑒𝑟𝑒:
𝑥 𝑚 = 𝑐𝑙𝑎𝑠𝑠 𝑚𝑎𝑟𝑘
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

22. Example 1. Compute the mean of the scores
of the students in a Mathematics IV test.

23. Solution in Example 1:
i=5 𝑓=48 𝑓𝑥 𝑚=1549

24. Example 2. Compute the mean of the scores
diagnostic test of Grade 9 Narra students.
Class
Interval
f 𝑥 𝑚 𝑓𝑥 𝑚
36 – 40 1
31 – 35 10
26 – 30 10
21 – 25 16
16 – 20 9
11 – 15 4
i=5 𝑓=50 𝑓𝑥 𝑚=1230
𝑥 =
𝑓𝑥 𝑚
𝑓
𝑥 =
1230
50
𝒙 = 𝟐𝟒. 𝟔

25. TRY THIS. Compute the mean of the height of
IV-1 and IV-2 Students
Class
Interval
f 𝑥 𝑚 𝑓𝑥 𝑚
175 – 179 2
170 – 174 5
165 – 169 8
160 – 164 11
155 – 159 21
150 – 154 14
145 – 149 17
140 – 144 2
i=5 𝑓=80 𝑓𝑥 𝑚=12540
𝑥 =
𝑓𝑥 𝑚
𝑓
𝑥 =
12540
80
𝒙 = 𝟏𝟓𝟔. 𝟕𝟓

26. GRADED ASSESSMENT:
Find the mean of each grouped data.
1

27. GRADED ASSESSMENT:
2

28. GRADED ASSESSMENT:
3

29. MEDIAN of Grouped Data
REMEMBER!

30. Example 1. Compute the median of the scores of the
students in a Mathematics IV test.
Class
Interval
f < 𝑐𝑓
46 – 50 1 48
41 – 45 5 47
36 – 40 11 42
31 – 35 12 31
26 – 30 11 19
21 – 25 5 8
16 – 20 2 3
11 – 15 1 1
i=5 𝑓=48
Median Class:
=
48
2
= 24𝑡ℎ
MC

31. Example 2. Solve for the median gross sale
of Aling Mely’s Sari-sari Store for one month.
Class
Interval
f < 𝑐𝑓
1,001 – 1,500 1 1
1,501 – 2,000 1 2
2,001 – 2,500 3 5
2,501 – 3,000 7 12
3,001 – 3,500 5 17
3,501 – 4,000 6 23
4,001 – 4,500 4 27
4,501 – 5,000 3 30
i=500 𝑓=30
Median Class:
=
30
2
= 15𝑡ℎ
MC

32. TRY THIS! Non-Graded Activity
Solve for the median of Scores of Diagnostic
Test of IV-Narra Students .
Class
Interval
f < 𝑐𝑓
36 – 40 1 50
31 – 35 10 49
26 – 30 10 39
21 – 25 16 29
16 – 20 9 13
11 – 15 4 4
i=5 𝑓=50
Median Class:
=
50
2
= 25𝑡ℎ
MC
20.5
50
13
16
5
Md=24.25

33. GRADED ASSESSMENT:
Find the Median of the following grouped data.
1

34. GRADED ASSESSMENT:
Find the Median of the following grouped data.
2

35. MODE of Grouped Data
The mode of grouped data can be approximated using the
following formula:
REMEMBER!

36. Example 1. Compute the MODE of the scores of the
students in a Mathematics IV test.
Class
Interval
f
46 – 50 1
41 – 45 5
36 – 40 11
31 – 35 12
26 – 30 11
21 – 25 5
16 – 20 2
11 – 15 1
i=5
Modal Class:
= 31 − 35
Mo

37. Example 2. Solve for the MODE gross sale of Aling Mely’s
Sari-sari Store for one month.
Class Interval f
1,001 – 1,500 1
1,501 – 2,000 1
2,001 – 2,500 3
2,501 – 3,000 7
3,001 – 3,500 5
3,501 – 4,000 6
4,001 – 4,500 4
4,501 – 5,000 3
i=500
Modal Class:
= 2501 − 3000
Mo

38. TRY THIS.
Compute the MODE of the height of IV-2 Students
Height in cm f
175 – 179 2
170 – 174 5
165 – 169 8
160 – 164 11
155 – 159 21
150 – 154 14
145 – 149 17
140 – 144 2
i=5
Modal Class:
= 155 − 159
Mo
𝑙𝑏 𝑚𝑜 = 154.5
𝐷1 = 21 − 14 = 7
𝐷2 = 21 − 11 = 10
𝑖 = 5
𝑀𝑜 =156.56

39. GRADED ASSESSMENT:
Find the Mode of the following grouped data.
1

40. GRADED ASSESSMENT:
Find the Mode of the following grouped data.
2