Resources in Mathematics

1. Maria Diza C. Febrio
BAYUGAN NATIONAL COMPREHENSIVE HIGH SCHOOL
Bayugan City
mariadizafebrio@gmail.com
Created by:

2. Read the Instructions First
INTRODUCTION
DISCUSSIONS AND
EXAMPLES
OBJECTIVES
EXERCISES AND
CHALLENGES

3. 1. This material is designed to help you solve the Measures of Central
Tendency (Ungrouped): mean, median and mode with each examples and
exercises.
2. Just click the ff. icons at the bottom of the slides.
- click this icon if you want to go the to the previous slide.
- click this icon if you want to go to the next slide.
- click this icon if you want to show the home page or the menu.
3. Click the following at the homepage or at the menu.
- it shows you the background of the topic.
- it shows you what will be the outcome after learning
this material.
- it contains all about the topic with
examples to deepen your understanding.
- to measure your learning after you read
the topics.
4. In exercises, its just a multiple choice. Click the letter of your answer.
Solutions also were provided if you got the correct answer.
5. Enjoy learning.
INSTRUCTIONS
INTRODUCTION
OBJECTIVES
DISCUSSIONS AND
EXAMPLES
EXERCISES AND CHALLENGES

4. Measures of Central Tendency
are a key way to discuss and communicate
with graphs. The term central tendency refers to
the middle, or typical, value of a set of data,
which is most commonly measured by using the
three m's: mean, median, and mode. The mean,
median, and mode are known as the measures of
central tendency.
INTRODUCTION

5. The learners can develop their
understanding of the measures of central
tendency ;
This topic is best for Grade 7 and Grade 8 learners.

6. often called the average, of a
numerical set of data, is simply the sum
of the data values divided by the
number of values. This is also referred to
as the arithmetic mean. The mean is the
balance point of a distribution.

9. When the totals of the list are odd, the median is
the middle entry in the list after sorting the list
into increasing order. When the totals of the list
are even, the median is equal to the sum of the
two middle (after sorting the list into increasing
order) numbers divided by two. Thus, remember
to line up your values, the middle number is the
median! Be sure to remember the odd and even
rule.

10. The mode of a set of data is simply the value
that appears most frequently in the set. If two or
more values appear with the same frequency, each
is a mode. The downside to using the mode as a
measure of central tendency is that a set of data
may have no mode, or it may have more than one
mode. However, the same set of data will have only
one mean and only one median.

12. A. Find the mean for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
Use the formula in computing the mean:
Solution:
= sum of the values =
the number of values
Mean ( 13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13)
9
=
= is the mean

18. Subject Number of Units Grade
English 3 93
Filipino 3 87
Math 3 94
Science 5 92
P.E. 1 86
Social Studies 3 88

23. 76, 81, 79, 80, 78, 83, 77, 79, 82, 75
There is no need to organize the data, unless
you think that it would be easier to locate the mode if
the numbers were arranged from least to greatest. In
the above data set, the number 79 appears twice, but
all the other numbers appear only once. Since 79
appears with the greatest frequency, is the mode
of the data values and it is the only value that occurs
most often, the set is called

24. J. The ages of 12 randomly selected customers at a local Best Buy are listed
below:
23, 21, 29, 24, 31, 21, 27, 23, 24, 32, 33, 19
What is the mode of the above ages?
The above data set has three values that each
occur with a frequency of 2. These values are
21, 23, and 24. All other values occur only
once. Therefore, this set of data has three
modes which are 21, 23 and 24 and the set is
called multimodal.

25. 1. What is the Mean of these numbers?
6, 11, 7 ?
 Multiple Choice:
A. Choose the letter of your answer.
8 4
5
c
b
a
d 7

26. 2. Scott took 7 math tests in one marking period.
What is the mean test score?
89, 73, 84, 91, 87, 77, 94
64 91
85
a
b
c
d 83

27. 3. Mark operates Technology Titans, a Web site
service that employs 8 people. Find the mean age
of his workers if the ages of the employees are as
follows: 55, 63, 34, 59, 29, 46, 51, 41
a
b
c47.25 31.50
50.04 d 43.25

28. 4. Find the median of this set of data.
20, 30, 35, 24, 36, 47, 48
a
b
c35 47
36
d 44

29. 5.) What is the mode in this given data?
2, 5, 4, 1, 6, 7, 4, 3, 2, 1
a
b
c1 & 2 1,2 &4
2 & 4 d 1 & 4

30. 6.) The scores of 10 students in a 5-item
quiz are 2, 2, 3, 3, 4, 4, 4, 4, 4, 5. What is the
mode?
a
b
c4 2
3 d 5

31. 7.) The daily wages of 5 workers are as
follows : Php 350, Php 400, Php 400, Php
500, Php 450. Find the mean daily wage.
a
b
cPhp 500 Php 350
Php 320 d Php 420

32. 8.)Find the median of these grades.
90, 84, 79, 80, 77, 89, 95, 93, 90, 86, 85
a
b
c90 93
86 d 80

33. 9.) Find Nielzen’s grade point average.
c
Subject Number of Units Grade
English 3 91
Filipino 3 89
Math 3 93
Science 5 88
Value Ed. 2 92
PE 1 93

34. a
b
c89.16 90.35
88.00 d 91.25

35. 10.)Find the median of these grades : 80, 78,
81, 83, 95, 85.
a
b
c83 95
80 d 82

36. B. Find the mean, median and mode of the given data.
11. ) 13, 13, 10, 8, 7, 6, 4, 5
mean
a.
b.
c.
8
8.25
7.25
d. 6.50

37. 12. ) 13, 13, 10, 8, 7, 6, 4, 5
median
a.
b.
c.
10
8.25
7.50
d. 13

38. a.
b.
c.
mode
13. ) 13, 13, 10, 8, 7, 6, 4, 5
13
10
5
d. 8

39. a.
b.
c.
mean
144.17
136.25
140.15
14.) 130, 140, 135, 125, 160, 175
d. 140.25

40. a.
b.
c.
median
140
136
135
15. ) 130, 140, 135, 125, 160, 175
d. 130

41. a.
b.
c.mean
91
95
88
16. Vic’s scores in three unit tests are 92, 87,
and 88. What must his score be on the fourth
test to get an average of 90?
d. 93

42. a.
17. The number of jeepney passengers for
each trip of Mang Dante’s jeepney is recorded
as follows: 10, 12, 8, 14, 10, 16, 13, 15, 10. Find
the mean number of passengers.
b.
c.
d.
12
14
13
10
mean

43.  Directions: For numbers 18-20, refer to
the given data below.
The prices of a yellow shirt in 9 stores are
surveyed and the results are as follows:
Php 80, Php 100, Php 120, Php 120, Php 130,
Php 140, Php 150, Php 675, Php 2200

44. a.
b.
c.
median
Php100
Php150
Php120
18.) Find the median.
Php 80, Php 100, Php 120, Php 120, Php 130,
Php 140, Php 150, Php 675, Php 2200
d. Php130

45. a.
b.
c.
mean
640.40
412.78
500.12
19.) Find the mean.
Php 80, Php 100, Php 120, Php 120, Php 130,
Php 140, Php 150, Php 675, Php 2200
d. 120.33

46. a.
b.
c.
mode
675
150
100
20.) Find the mode.
Php 80, Php 100, Php 120, Php 120, Php 130,
Php 140, Php 150, Php 675, Php 2200
d. 120

47. Solution:
1. a
Mean = 6 + 11 + 7
3
= 24
3
= 8
A.

48. Solution:
2. b
Mean = 89 + 73 + 84 + 91 + 87 + 77 + 94
7
= 595
7
= 85

49. Solution:
3. a
Mean age of = 55 + 63 + 34 + 59 + 29 + 46 + 51 + 41
Mark’s worker 8
= 378
8
= 47.25

50. Solution:
4. a
1. Arrange the data (increasing order).
20, 24, 30, 35, 36, 47, 48
2. Since this is odd, the median is the
middle number.
20, 24, 30, 35, 36, 47, 48
the median is 35.

51. Solution:
5. c
2, 5, 4, 1, 6, 7, 4, 3, 2, 1
Since the numbers 1, 2 and 4 appeared with the
same frequency therefore these set of numbers is the
mode.
Modes: 1, 2 and 4

52. Solution:
6. a
2, 2, 3, 3, 4, 4, 4, 4, 4, 5
Since the number 4 occurs frequently in the
data therefore the mode is 4.

53. Solution:
7. d
Mean daily wage = 350+400+400+500+450
5
= 2100
5
= Php 420

54. Solution:
8. b
1. Arrange the data (increasing order).
77, 79, 80, 84, 85, 86, 89, 90, 90, 93, 95
2. Since this is odd, the median is the
middle number.
77, 79, 80, 84, 85, 86, 89, 90, 90, 93, 95
the median is 86

55. Solution:
9. c
GPA = 91(3)+89(3)+93(3)+88(5)+92(2)+93(1)
3+3+3+5+2+1
= 1536
17
= 90.35

56. Solution:
10. d
1. Arrange the data (increasing order).
78, 80, 81, 83, 85, 95
2. Since this is even, identify the two middle number
then add and divide it by two.
78, 80, 81, 83, 85, 95
= 81 + 83 = 164 = 82 is the median
2 2

57. Solution:
11.b
Mean = 13 + 13 + 10 + 8 + 7 + 6 + 4 + 5
8
= 66
8
= 8 . 25
B.

58. Solution:
12. c
1. Arrange the data (increasing order)
4, 5, 6, 7, 8, 10, 13, 13
2. Since this is even, identify the two middle number
then add and divide it by two.
4, 5, 6, 7, 8, 10, 13, 13
= 7 + 8 = 15 = 7.50
2 2

59. Solution:
13. a
Mode:
4, 5, 6, 7, 8, 10, 13, 13
Which number appeared most often?
13, therefore this is the mode.

60. Solution:
14. a
Mean = 130 + 140 + 135 + 125 + 160 + 175
6
= 865
6
= 144.17

61. Solution:
15. c
Median
1. Arrange the data (increasing order).
125, 130, 135, 140, 160, 175
2. Since this is odd, the middle value is
the median.
125, 130, 135, 140, 160, 175

62. Solution:
16. d
Let x be his score on the fourth test.
Sum of the four scores = mean x 4
= 90 x 4
= 360
So, 92+ 87+88+x = 360
267+x = 360
x = 360 – 267
= 93 score needs by Vic

63. Solution:
17. b
Mean number of passengers = 10 + 12 + 8 + 14 + 10 + 16 + 13 + 15 + 10
9
= 108
9
= 12

64. Solution:
18. d
1. Arrange the data (increasing order).
Php 80, Php 100, Php 120, Php 120, Php 130,
Php 140, Php 150, Php 675, Php 2200
2. Since this is odd, the middle value is the median.
Php 80, Php 100, Php 120, Php 120, Php 130,
Php 140, Php 150, Php 675, Php 2200

65. Solution:
19. a
Mean = 80+100+120+120+130+140+150+675+2200
9
= 3715
9
= 412.78

66. Solution:
20. d
Php 80, Php 100, Php 120, Php 120, Php 130,
Php 140, Php 150, Php 675, Php 2200
Since the number 120 occurs frequently in the
data therefore the mode is 120.

67. Solution:
1. a
Mean = 6 + 11 + 7
3
= 24
3
= 8

69. Solution:
1. a
Mean = 6 + 11 + 7
3
= 24
3
= 8
QUIT

70. This a Multiple Choice Test. You should be
able to perform at least Proficient level.
Advanced - 16 - 20 pts.
Proficient - 12 - 15 pts.
Approaching Proficiency - 8 - 11 pts
Developing - 4 - 7 pts.
Non-Proficient - 0 - 3 pts.
If your performance is below Proficient level, read the
topic and answer the exercises again. Proceed!

71. Problem Solving:
Direction: Solve this problem in your own.
Two weeks before Mark opened
Technology Titans, he launched his company
Web site. During those 14 days, Mark had an
average of 24.5 hits on his Web site per day. In
the first two days that Technology Titans was
open for business, the Web site received 42 and
53 hits respectively. Determine the new average
for hits on the Web site.