I. Objectives

            At the end of the period, the students are expected to:

1. Define mean, median and mode

2. Compute the mean, median and mode of the given set of data and

3. Relate mean, median and mode on real life situation.

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II. Subject Matter

A. Topic: Measures of Central Tendency of Ungrouped Data

B. Concept/Ideas: There are three measures of central tendency: the mean, median and mode. To compute for the mean, add all the given data and divide it to the number of data given. For the median, if the number of ordered raw data is odd, the median is in the middle position, and if even, the mean of the two middle data of an ordered data is the median. The number that appears most often in a collection is the mode.

C. Process: Computing, Analyzing

D. References: Mathematics Learner’s Module, pp. 491-496

Orence, O. A. and Mendoza, M. D. (2010) E-math Advanced Algebra and Trigonometry. Rex Printing Company Inc. 84-86 P. Florentino St., Sta. Mesa Heights, Quezon City

E. Materials: marker, laptop, speaker, projector

F. Value Focus:Cooperation/Collaboration

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III. Learning Activities

Part of the Lesson:

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(Prayer): Good morning class, please all stand and we will start our class with a prayer. So, may I request one representative to lead the prayer.​

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(Energizer): Please remain standing and we will be having our ice breaking or the energizer. I have here a dance and I want everyone to dance. May I request everyone to stand?

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(Review):

So as discussed last meeting, we tackled about. Parallelism. As a review,

 

How can we say that the two lines are parallel?

 

What is transversal line?

 

The angles formed by transversal with the two other lines are called?

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(Motivation):

Who loves reading poems? Okay. I have here a poem. I want you to recite the poem after me. Okay?

 

Hey diddle, diddle, the medians

The middle

You add and divide

For the mean

The mode is the one

That you see the most

Central tendency begins!

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(Presentation): Okay this time, I will group you into 3.

Now go to your respective groups and answer the given questions to get the answer. I will give you 5 minutes to answer.

 

1. The first three letters is sometimes the name of a street.

2. The third, fourth and fifth letter is all about time from the past.

3. The fifth, sixth and seventh letter are years.

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(Analysis): Item number 1 states that the first three letters is sometimes the name of a street. So the answer is AVE from the word avenue.

 

In item number 2 states that the third, fourth and fifth letter is all about time from the past. The answer is ERA.

 

And in item number 3 states that the fifth, sixth and seventh letter are years and that is AGE.

If we combine this three, we get AVERAGE!

 

Our lesson for today is related to the word average.

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(Discussion/Abstraction): What are the measures of central tendency?

A measure of central tendency (also referred to as measures of centre or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or centre of its distribution.
There are three main measures of central tendency: the mode, the median and the mean. Each of these measures describes a different indication of the typical or central value in the distribution. 

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What is the mean?
The mean is the sum of the value of each observation in a dataset divided by the number of observations. This is also known as the arithmetic average. 
Looking at the set retirement age: 

54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

The mean is calculated by adding together all the values (54+54+54+55+56+57+57+58+58+60+60 = 623) and dividing by the number of observations (11) which equals 56.6 years.
 

What is the median?
The median is the middle value in set of data when the values are arranged in ascending or descending order.
The median divides the data in half (there are 50% of observations on either side of the median value). In a distribution with an odd number of observations, the median value is the middle value. 
Looking at the retirement age data (which has 11 observations), the median is the middle value, which is 57 years: 

54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60 

When the data has an even number of observations, the median value is the mean of the two middle values. In the following distribution, the two middle values are 56 and 57, therefore the median equals 56.5 years: 

52, 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

What is the mode?
The mode is the most commonly occurring value in a given set of data.
Consider this data set showing the retirement age of 11 people, in whole years:

54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60

The most commonly occurring value is 54, therefore the mode of this distribution is 54 years. 

 

(Generalization):Let’s check if you really understand our lesson.

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How do we get the mean?

  

How do we get the median?

 

How about mode?

 

Well said class. I have here a math song, and I required everyone to sing this math song.

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(Application):

This time, you will have a game. Go to your respective group please.

 

Do you know the game the boat is sinking?

This game is like, you were assigned one number for you. For example, 1. When I say, the boat is sinking the boat is sinking, save number 1, so the one that got the number one will be save by the cooperation of the groupmates. The body or any part of the body of that student can’t be touch on the floor. You can lift that student, or do some tricks in order to save that person.

 

On the other hand, we will give it a twist. Instead of numbers, I will give you the answer. It goes this way, I will say, the boat is sinking, the boat is sinking, save _____. Instead of number, I will ask question. And you will answer that question and save the person who is assigned with that answer. Are we clear?

The group that got the correct answer will have a point.

 

Okay let’s rock!

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(Evaluation):

Get your notebook and the problem.

 

A student has gotten the following grades on his subject 87, 87, 92, 90, 85, 83. Find the

1. Mean

2. Median

3. Mode

 

You have 5 minutes to finish your work.

Time’s up! Pass your work in front.

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(Assignment):

Let’s practice at home!

Problem: the set of data shows a score of 25 students in their periodical test.

 

34    35    40    40    48

21    20    19    34    45

19    17    18    15    16

21    20    18    17    18

 

Find the following:

1. Mean

2. Median

3. Mode

 

That’s all for today! Good bye class.