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1. Republic of the Philippines
DEPARTMENT OF EDUCATION
Region XI
DIVISION OF DAVAO CITY
Davao City
DAVAO CITY NATIONAL HIGH SCHOOL
F. Torres St., Davao City
Telefax No. (082) 227 9102
LESSON PLAN IN MATHEMATICS 7
Topic: Measures of Central Tendency of Ungrouped Data
Content Standard
The learner demonstrates understanding of key concepts, uses and
importance of statistics , data collection/gathering and the different forms
of data representation, measures of central tendency, measures of
variability, and probability.
Performance Standards
The learner is able to collect and organize data systematically and compute
accurately measures of central tendency and variability and apply these
appropriately in data analysis and interpretation in different fields.
Learning Competency
Calculates measures of central tendency of a statistical data ungrouped data
(M7SP-IVh-i-1)
I. Objectives
By the end of the lesson, the learners will be able to:
a. define mean, median and mode ;
b. calculate mean, median and mode of a statistical data of ungrouped data;
c. show appreciation to the value of mean, median, and mode in real life
II. Subject Matter
1. Topic: Measures of Central Tendency of Ungrouped Data
2. References: K to 12 Mathematics Curriculum Guide (M7SP-IVh-i-1)
Grade 7 Mathematics Module 4 – Quarter 4
2. 3. Materials: Laptop , Cellphone,Self –Learning Module, Google Meet, and
Powerpoint Presentation
III. PRELIMINARIES
1. Prayer
2. Greetings
3. Checking of Attendance
4. Online classroom rules
IV. LESSON PROPER
Motivation
A letter from Never Land
Activity
Activity: THREE TREASURE CHESTS HUNT!
Direction: Analyze the given situation. Show you solution.
Level 1
1. 3, 4, 2, 6,1 ,2
The number that represent these numbers is 3. How did you come up
with 3?
2. 7, 6, 9, 7, 10, 8,9,5 ,15, 8
The number that represent these numbers is 8.4. How did you come
up with 8.4?
3. 13,4,8,5,2, 15,9, 3
Help! We need to get the three treasure chests, to win against Captain Hook. In order to do that,
we challenge you to undergo three level of challenges.
Every finished challenge will give you one treasure chest and the magical code. We need to get
those magical code to open the treasure chests to conquer Captain Hook.
3. The number that represent these numbers is 7.375. How did you
come up with 7.375?
The Magical Code is MEAN.
Level 2
1. 3, 5, 8,16,20
The number that represent these numbers is 8. How did you come
up with8 ?
2. 2, 4, 6, 9, 13, 12, 5
The number that represent these numbers is 5. How did you come
up with 5?
3. 1, 2,4,5, 7, 10
The number that represent these numbers is 4.5. How did you come
up with 4.5?
The Magical Code is MEDIAN.
Level 3
1. 30, 30, 42, 48, 55, 67
The number that represent these numbers is 30. How did you come
up with 30?
2. 24, 89, 4,23,23,7, 1, 23
The number that represent these numbers is 23. How did you come
up with 23?
3. 45, 2, 9, 25, 11,11, 45
The number that represent these numbersare 11 and 45. How did you
come up with11 and 45?
The Magical Code is MODE.
Analysis
1. How did you find the activity?
2. Did all the levels of challenges can be solve in the same way?
3. How did you solve the given situation on each level of the challenges?
4. Abstraction
The mean (also known as the arithmetic mean/average) is the most
commonly used measure of central position. It is the sum of measures x
divided by the number N of measures in a variable. It is symbolized as X
̅
(read as “X- bar”).
To find the mean of an ungrouped data, use the formula
𝑋̅ =
𝜮𝒙
𝑵
where 𝑋̅ read as “X–bar” for the mean,
Σx = the summation of x (sum of the measures) and
N is the number of values in the data set.
The median is the middle value in a set of data.
It is symbolized as (𝑋̃ ) (read as “X– tilde”).
To find a median, arranged the scores either in increasing or decreasing order
and then find the middle score
Example 1:
Find the median of the following set of numbers.
8 , 14, 8, 45, 1, 31, 16, 40, 12, 30, 42, 30, 24
1, 8, 8, 12, 14, 24, 30, 31, 40, 42 - The median is 24.
5. In case of an even number of terms the average of the middle values is the
median.
𝑋̃ =
𝒙𝟏+𝒙𝟐
𝟐
𝐄𝐱𝐚𝐦𝐩𝐥𝐞 𝟐:
5, 1𝟔, 𝟗, 𝟑,𝟕, 𝟏𝟒, 𝟏𝟏, 𝐚𝐧𝐝 𝟒
3,4,5,7,9, 11, 14, 16
𝑋̃ =
𝑥1+𝑥2
2
𝑋̃ =
7+9
2
𝑋̃ =
16
2
= 8
The median is 8.
The mode is the measure or value which occurs most frequently in a set of
data. It is the value with the greatest frequency.
It is symbolized as (𝑋̃) (read as “X–hat”).
To find the mode for a set of data:
1. select the measure that appears most often in the set;
2. if two or more measures appear the same number of times, then each of
these values is a mode; and
3. if every measure appears the same number of times, then the set of data
has no mode.
6. Example 1:
2, 3, 8, 19, 24, 24, 58 60
The mode is 24 .
Select the measures appears most often in the set of data.
Example 2:
23, 21, 16, 22, 19 , 24 .
If every measure appears the same number of times , then the set of data has
no mode. Therefore, there is no mode for this example.
Example 3:
18, 20, 16, 18, 15, 19, 17, 20
The mode are 18 and 20.
If two or more measures appear the same number of times, then each of
these values is a mode
Generalization
MEAN- Adding all the numbers and get the quotient of the sum by dividing
the number of how many number given.
Formula ,
MEDIAN - Median is the middle number in the list of numbers ordered from
lowest to greatest.
x ̅=
∑𝒙
𝑵
In case if even, x ̅=
𝑿𝟏+𝑿𝟐
𝟐
7. MODE- Mode is the value that appears most often in a set of data.
1. Select the measure that appears most often in the set;
2. If two or more measures appear the same number of times, then
each of these values is a mode;
3. If every measure appears the same number of times , then the set
of data has no mode.
Application
The teacher will give an activity related to the real life situation. Students
will submit their answers in classpoint.app.
Direction: Analyze and solve the problem. Show your solution.
1. Th𝑒 𝑅𝑜𝑦𝑐𝑒 𝑔𝑎𝑠 𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑜𝑤𝑛𝑒𝑟 𝑟𝑒𝑐𝑜𝑟𝑑𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠
𝑤ℎ𝑖𝑐ℎ 𝑣𝑖𝑠𝑖𝑡 ℎ𝑖𝑠 𝑝𝑟𝑒𝑚𝑖𝑠𝑒𝑠 𝑓𝑜𝑟 12 𝑑𝑎𝑦𝑠. 𝑇ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑟𝑒:
𝟑𝟎𝟒, 𝟐𝟕𝟗, 𝟑𝟏𝟒,𝟐𝟓𝟕, 𝟑𝟎𝟐,𝟐𝟐𝟑, 𝟐𝟒𝟗, 𝟐𝟏𝟎, 𝟐𝟖𝟗, 𝟑𝟎𝟐, 𝟐𝟎𝟗, 𝟐𝟗𝟎.
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑚𝑒𝑎𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠 𝑝𝑒𝑟 𝑑𝑎𝑦.
2. John met 7 milktea vendors in Davao City. John is planning to have a
milktea shop business therefore he asked them about their monthly profit.
John found out that the profitt were:
Php28, 000, Php 35, 000, Php 39,000, Php 6,500, Php32,000, Php 25, 000
and Php 25, 500. What would be the mean ?
3. The following are the ages of students in a vocational class:
8. 32, 43, 39, 28, 42, 31. Find the median ages of the students.
4. Samuel is planting pepper plants in his garden. He wants to know how
many plants he will need to feed his family. Lest year Samuel recorder
how many peppers each plant produced . Here are his results:
8,5, 9, 6, 4, ,3 ,7, 5, 3, 5, 9, 3
To help Samuel determine how many peppers he can expect each plant to
produces let’s calculate the median and mode.
Evaluation
Students will submit their answers in classpoint.app.
I. Define the following:
1. Mean 2. Median 3. Mode
II. Find the mean, median and mode and interpret the results.
1. Determine the mean of the following set of numbers:
36, 87, 56, 75 , 110, 89, 54, 61
2. A student recorded her scores on weekly math quizzes that were
marked out of possible ten points her scores a follows:
8, 6, 6, 7, 9, 6, 9, 9, 8, 8, 7, 5, 9, 7 , 5, ,5 ,5 8, 6
What is the median and mode of her scores on the weekly math
quizzes ?
III. Give a real life scenario where measures of central tendency will
be applied.
