School:
Pre-service Teacher:
Teaching Dates and Time:
Grade Level / Section:
11- MAXTHON/ 11- NETSCAPE/ 11- YANDEX
STATISTICS AND PROBABILITY
Learning Area:
DAILY LESSON
PLAN
I.OBJECTIVES
A. Content
Standards:
INOCENCIO V. FERRER MEMORIAL SCHOOL OF
FISHERIES
LLOYD DEXTER D. ALLA
Quarter:
THIRD QUARTER/SECOND SEMESTER
The learner demonstrates an understanding of key concepts of random variables and
probability distributions.
B. Performance
Standards:
The learner is able to apply an appropriate random variable for a given real-life problem
(such as in decision-making and games of chance).
C. Learning
Competencies/
Objectives:
Calculates the standard deviation of a discrete random variable.
(M11/12SP-IIIb-2)
Write the LC Code for each
II. CONTENT
MEASURES OF VARIABILITY
(STANDARD DEVIATION)
III. LEARNING
RESOURCES
A. REFERENCES
1. Teacher’s Guide
pages
2. Learner’s
Material pages
3. Textbook Pages
4. Additional
Materials from
Learning
Resource (LR)
portal
B. Other Learning
Resources
IV. PROCEDURES
A. Preparatory
Activities
B. Reviewing
Previous Lesson or
Presenting the New
Lesson
Mathematics Learner’s Material
General Statistics 3rd Edition (pp 88-90)
E- Math Worktext
https://youtu.be/gpKEfVZlPj4



PRAYER
GREETINGS
CHECKING OF ATTENDANCE
REVIEW
Recall the Mode of Ungrouped and Grouped Data

What is the mode?
The mode is the most occurred value/ number of observations which is often the most.
C. Establishing a
Purpose for the
Lesson
D. Presenting
Examples/Instances
of the Lesson

What are the four types of modes?
Unimodal- only one mode
Bimodal- two modes
Trimodal- three modes
Multimodal- three or more modes.

What is the formula for the mode for grouped data?
𝑑1
𝑥̂ = 𝐿𝐵𝑚𝑜 + (
)𝑖
𝑑1 + 𝑑2
Where:
𝑥̂- mode
𝐿𝐵𝑚𝑜 - lower boundary of the modal class
𝑑1 - difference between the frequency of the class below the modal class
𝑑2 - difference between the frequency of the class above the modal class
𝑖- interval/ class

What are the steps in finding the mode using grouped data with the given frequency and
class interval?
1. Determine the modal class.
2. Determine the lower boundary of the modal class.
3. Find the differences 𝑑1 and 𝑑2 .
4. Determine the interval or class width.
5. Substitute the given values to the formula for the mode.
(The students read the objectives)
By the end of this lesson, the students should be able to:
 define standard deviation,
 relate the importance of standard deviation, and
 solve the standard deviation using ungrouped data.
Activity 1
The teacher prepares the WORD PUZZLE on the board. From the puzzle, find and encircle the
words that are usually used in statistics. And I will choose 5 students to come in front to find and
encircle the words.
Q
W E
R
T
Y
U
I
O
P
L
M A
S
D
F
G
H
J
K
E
Z
X
C
R
V
B
N
M Q
D
W E
N
R
A
T
Y
M U
I
I
O
A
P
A
N
S
O
D
A
F
G
E
H
J
K
G
D
L
N
Z
X
M C
V
B
N
E
M
A
S
D
F
G
H
J
K
L
Q
W F
R
E
Q
U
E
N
C
Y
E
T
Y
U
I
O
P
A
S
R
The teacher prepares the video about the standard deviation.
D. Discussing New
Concepts and Practicing
New Skills #1
(The teacher will ask the students about the video.)
MEASURES OF VARIABILITY
Standard Deviation
- is the measure of the variability of a set of data in terms of the amounts by which the
individual values differ from their mean.
- A high standard deviation means that values are generally far from the mean, while a low
standard deviation indicates that values are clustered close to the mean.
The formula of the standard deviation of ungrouped data is:
∑(𝑥 − 𝑥̅ )2
𝑆=√
𝑛
Where:
S= standard deviation
𝑥 - observed value
𝑥̅ – mean
(𝑥 − 𝑥̅ )- deviation from mean
∑(𝑥 − 𝑥̅ )2 – sum of squared deviation
n- number of observation/ cases
Steps to find the standard deviation:
1. Find the mean of the given values. (𝑥̅ =
2.
3.
4.
5.
𝛴𝑥
)
𝑛
Find the deviation of each value from the mean.
Square each deviation from Step 2.
Find the sum of the squared deviation in Step 3.
Substitute the given values in the formula of standard deviation.
Example 1: Find the standard deviation of the following set of data.
The following scores in Math 9 exams are: 40, 45, 55, 65, 70, 75, 80, 85, 90, and 95.
𝑥
40
45
55
65
70
75
80
85
90
95
Σ𝑥 = 700
(𝑥 − 𝑥̅ )
-30
-25
-15
-5
0
5
10
15
20
25
𝛴𝑥
𝑛
700
=
10
𝑥̅ = 70
(𝑥 − 𝑥̅ )2
900
625
225
25
0
25
100
225
400
625
∑(𝑥 − 𝑥̅ )2 = 3150
∑(𝑥 − 𝑥̅ )2
𝑆=√
𝑛
𝑥̅ =
3150
=√
10
= √315 ≈ 17.75
𝑆 = 18
E. Discussing New
Concepts and Practicing
New Skills #2
Let’s have another example.
Find the standard deviation of the following data: 8, 9, 10, 12, 17, 18, 18, 19, 20, 21
𝑥
8
9
10
12
17
18
18
19
20
21
Σ𝑥 = 152
𝛴𝑥
𝑛
152
=
10
𝑥̅ = 15.2
𝑥̅ =
(𝑥 − 𝑥̅ )
-7.2
-6.2
-5.2
-3.2
1.8
2.8
2.8
3.8
4.8
5.8
(𝑥 − 𝑥̅ )2
51.84
38.44
27.04
10.24
3.24
7.84
7.84
14.44
23.04
33.64
∑(𝑥 − 𝑥̅ )2 = 217.6
∑(𝑥 − 𝑥̅ )2
𝑆=√
𝑛
217.6
=√
10
= √21.76 ≈ 4.67
𝑆=5
F. Developing Mastery
(Leads to Formative
Assessment 3)
G. Finding Practical
Applications of Concepts
and Skills in Daily Living
Let’s have a seatwork. Answer in 10 minutes.
Find the standard deviation of the following data: 3, 10, 21, 12 and 4.
This time, let us proceed with our next activity.
Activity 2
The class will be divided into two groups. Each group must have a group leader to present your
work. The teacher will provide manila paper and a pen per group. Each group will only be given
15 minutes to do the activity and then 5 minutes to present their work.
Find the standard deviation of the given data sets.
Group 1:
The ages of the 6 Math instructors in ABC College are : 50, 39, 40, 45, 38, 40.
Group 2:
The grades of 5 students in Calculus are : 85, 89, 94, 84 and 83.
Group 3:
The scores of Science test are: 90, 89, 95 and 88.
Rubric:
Criteria
Accuracy
H. Making
Generalizations and
Abstractions about the
Lesson
10
7
All computations are Some computations
accurate
and are erroneous and
complete.
incomplete
Legibility
Neat and visible at the Neat but not visible
back.
Cooperation
All the members are Some of the members
cooperate
are ccoperate
Oral Presentation
The group leader The group leader
speaks very clearly speaks clearly and
and well-explained
slightly explained
The teacher will ask recap questions about the lesson.
5
Most computations
are erroneous and
incomplete
Messy and not visble.
Most of the members
are not ccoperate
The group leader
speaks not clear and
no explanation.
1. What is standard deviation?
Standard Deviation- is the measure of the variability of a set of data in terms of the amounts
by which the individual values differ from their mean.
2. What is the formula for the standard deviation?
∑(𝑥 − 𝑥̅ )2
𝑆=√
𝑛
Where:
S= standard deviation
𝑥 - observed value
𝑥̅ – mean
(𝑥 − 𝑥̅ )- deviation from mean
∑(𝑥 − 𝑥̅ )2 – sum of squared deviation
n- number of observation/ cases
3. What are the steps to find the standard deviation?
Find the mean of the given values. (𝑥̅ =
𝛴𝑥
)
𝑛
Find the deviation of each value from the mean.
Square each deviation from Step 2.
Find the sum of the squared deviation in Step 3.
Substitute the given values in the formula of standard deviation.
4. Why is standard deviation important in real- life?
Possible Answer: Standard deviation is important in real-life because it is important to find
on how extend or gap in the data. In other fields, standard deviation is useful when getting
the extend and homogeneity of the area.
I. Evaluating Learning
(1 whole)
Find the standard deviation of the following set of data. (20 points)
J. Additional Activities
for Application or
Remediation
The scores of 7 students in Basic Calculus exam are: 46, 39, 42, 37, 45, 50, 51
The class will be divided into six groups. Each group will assign a grade level and sections. You can
ask the class advisers of each section about the number of students. Then find the standard
deviation of students per grade level.. Complete the table below and show your solution. Write it on
short-sized bondpaper.
Group 1- Grade 12
Names of Group Members:
Grade 12 Sections
Number of Students
Group 2- Grade 7
Names of Group Members:
Grade 7 Sections
Number of Students
Group 3- Grade 9
Names of Group Members:
Grade 9 Sections
Number of Students
Group 4- Grade 10
Names of Group Members:
Grade 10 Sections
Number of Students
Group 5- Grade 8
Names of Group Members:
Grade 8 Sections
Number of Students
Group 6- Grade 11
Names of Group Members:
Grade 11 Sections
REMARKS
V. REFLECTION
A. No. of learners who earned 80%
on the formative test
B. No. of learners who require
additional activities for remediation
C. Did the remedial lessons work?
No. of learners who have caught up
with lesson
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well? Why did this work?
F. What difficulties did I encounter
which my principal or supervisor can
help me solve?
G. What innovation or localized
materials did I use/discover which I
wish to share with other teachers?
Number of Students