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### Detailed Lesson Plan on Measures of Variability of Grouped and Ungrouped Data

• 1. DETAILED LESSON PLAN FOR DEMO TEACHING Grade 7 (Mathematics) Learning Competency: Calculates the measures of variability of grouped and ungroup data. I. OBJECTIVES At the end of the lesson, the students will be able to:  Identify the measures of variability of grouped and ungroup data.  Link the concept of measures of variability in real life context.  Solve the measures of variability of grouped and ungrouped data. II. SUBJECT MATTER Topic: Measures of Varibility of Grouped and Ungrouped data. Reference: Mathematics Module 7 Materials: Laptop, LCD Projector, Chalk, Activity Materials III. INSTRUCTIONAL PROCEDURE Teacher’s Activity Students’ Activity A. Daily Routine 1. Prayer Class let’s all stand up. Before we start, ___________ will lead the prayer. 2. Greetings Good Morning/ Good Afternoon class. Hi everyone, I am Junila A. Tejada Ma’am “June” in short and a graduate of BSED- Math. I am hoping for your outmost cooperation for todays lesson in order to make our lesson a success. Is that a deal class? 3. Checking of Attendance Is everybody present today? 4. Setting Expectation The teacher will present the lesson objectives. B. Priming / Activating Prior Knowlegde 1. Class, using your understanding of the concept of the “measures of central tendency”. Given the data below, find the mean of the data. A student will lead the prayer. Dear God, …….. Amen. Good Morning/ Good Afternoon Ma’am. Yes ma’am, deal. Yes ma’am, everybody is present today.
• 2. SET A: 4, 10, 12, 20, 24 SET B: 12, 13, 14, 15, 16 What is the mean for set A? How about for set B? 2. Review Based from the number line class, which set has a long line? How about short? Very Good. The line represent the spread of the data and it shows that Set A is more spread than Set B. Does the set of data in our activity can be considered as grouped or ungrouped data? Why? Very Good. Grouped data are set of data that are categorize and arrange in a form of data while the ungrouped data are data that are raw and not yet classified. C. Lesson Development 1. Motivation/ Activity Class, are you familiar with the term “measures of variability”? In our drill earlier, we compare the distance of spread of set A, and set B right? That process is a way of knowing the spread of the data and determining the consistency of data which is the core of the measures of variability, To learn more about the measures variability and its’ types we will conduct an activity. Are you ready? Let’s us start our activity entitled “Connectiword”. The class will be divided into six groups, each group will select their group leader. The activity is for only 5 minutes. Once the time is done, the students will submit their work. In the activity, the students will arrange the shuffled words by sequencing the clues indicated below the letter. Each group will select a representative that will The mean for set A ma’am is 14, while in Set B it is also 14. The set that has long line is Set A ma’am while the short line is Set B. It is ungrouped data ma’am because the data are not in table. The set of data is considered ungrouped ma’am. Students’ answers may vary. Yes we are ready. Yes ma’am.
• 3. pick the words to be arrange and a representative to recite the sequence that they created. Number 1: Number 2: Number 3: Number 4: Number 5: Number 6: 2. Analysis What did we do in our activity? Correct. What is the word for number 1? Kindly recite the description on each letter. The students will answer: The students will answer: The students will answer: The students will answer: The students will answer: The students will answer: We were tasked to arrange the letters base on the clues below the letter ma’am. The word ma’am is RANGE. A student will recite the steps in each letters.
• 4. Very Good. In order to find the spread of the scores of Mel, what did she discover? Exactly. The dicovery of Mel is the definition of range which we will? Very Good. What will be the range of the scores? Which set has less spread? Excellent. Therefore, the scores in Math class is more consistent and closer together. The formula above is applicable for grouped data. For group data, we will first get the upper boundary of the highest score and the lower boundary of the lowest score. What is the lowest score? What is the lowest boundary? The highest score and highest boundary? After identifying the lowest and highest Boundary, simply subtract the highest To the lowest boundary. So the range is? What if the two sets of data have the same range? Is there other way to compute the spread of the data? Let us find out later. What is the answer for the shuffled letter no. 2? Kindly recite the description below the letters. What did Joy find first? What is the mean? In subtracting the individual scores to the mean why it is important to get its absolute value? In mean deviation, we are concerned with the distance of the individual scores from the mean and there is no negative distance so we make sure to get is absolute value. So, if we will solve the mean deviation, we will create a table: She subtract the lowest score from the highest score ma’am. We will subtract the lowest score from the highest ma’am. The range of her score in Math is 5, while 8 in English ma’am. So the scores in math is less spread. The lowest score ma’am is 11 and the lowest boundary is 10.5, while the highest score is 22 and the highest boundary is 22.5. The range is 12 ma’am. Students’ answer may vary. The answer ma’am is MEAN DEVIATION. A student will recite the steps below the letters. The mean ma’am. The mean is 25 ma’am. The students’ answer may vary.
• 5. What will do next? Very Good. So our mean deviation is? Now, let us focus on number 3, what is the word? In the letter V, it indicates that it is a raw score, is data grouped or ungrouped? Correct. Kindly recite the description below the letter. Very Good. What is the first step of Veronica in finding the spread of her scores? After she find the difference of the mean and the individual score, what did she do with the result? So if we will get the variance, we will create a table. What is the summation of the squared over the number of terms? Very Good. Now what is the word for number 5? Please recite the description below the letters. What are your observation from the description recited? Exactly. Standard deviation (SD) is the squareroot of the variance, so the SD is? Now, we will proceed on the next word. What is the word for number 5? Okay. Kindly recite description below the letters. What is the first step? We will add the all the result and divide the number of terms. The mean deviation ma’am is 10. The word ma’am is VARIANCE. It is ungrouped data ma’am. A student will recite the steps below the letter. She first determines the mean ma’am. She squares the result ma’am. The variance is equal to 5. The word is STANDARD DEVIATION ma’am. A student will recite the steps below the letter. It is almost the same with variance ma’am but the standard deviation has square root. The standard deviation is 2.24. The word for number 5 ma’am is VARIANCE. A student will recite the steps below the letter. We need to find the class mark ma’am.
• 6. How can we find the class mark? Very Good. Now we will create a table. What is the summation of the f(x- mean)^2? Using the formula, what is our variance? What do you think is difference of this variance from the variance presented earlier? Very good. The formula earlier is for finding the variance for ungrouped data while this is the formula for finding the variance of grouped data. Now, we will reveal the last word. What is the word? Kindly recite the description underneath the letters. Do you have any observation? Very Good. In finding the standard Deviation of grouped data follow the Steps in finding the variance and find its squareroot. 3. Abstraction The terms that you discovered are the different measures of spread or measures of variability. Again, what is the purpose of measure of variability? Very good. Always remember that the lesser the variability, the more consistent the scores and the data. Now, what are the measures of variability for ungrouped data and grouped data? 4. Application By adding the two interval and dividing it by the number of terms. The summation ma’am is 420. The variance is 14.48 ma’am. The difference ma’am is that the data earlier are raw score while the data now contains interval and frequency. The word ma’am is STANDARD DEVIATION. A student will recite the steps below the letter. Yes ma’am. It is same with the steps in variance but final answer will be in square root. The measures of variability allows us to know how spread our scores/ data ma’am. The measures of variability for ungrouped and grouped data ma’am are range, mean deviation, variance, and standard deviation.
• 7. Now that you know the measures of varibility of grouped and ungrouped data, we will be having a group activity. I will divide you into two groups. Each group will select their group leaders. The leader will be the one who is responsible for dividing the task among the members of the group. Each group will be given a pen and a manila paper that consists of tables the goal of the group is to complete the table and answer the given questions. The activity will only cover 15 minutes of the time. 1. Complete the table below and find the: 1.1 Standard Deviation 1.2 Variance 1.3 Range 2. Complete the table below and find the: 2.1 Variance 2.2 Standard deviation The students will answer the ff: The students will answer the ff: The students will answer.
• 8. IV. Evaluation Class, write TRUE if the statement is true and FALSE if the statement is false. You have two minutes to answer this quiz. 1. The measures of variability allows us to determine the spread of the data. 2. The greater the variability, the more consistent the scores 3. In finding the range of ungrouped data, we will subtract the highest score to the lowest score. 4. In finding the range of the group data, we will subtract the highest class mark to the lowest class mark. 5 . The first step in getting the variance of grouped data is to determine the class boundary. 6. In finding the mean deviation, it is important to get the absolute value of (x-mean). 7. In finding the variance, we need to square root the result of (x-mean). 8. Standard deviation is the squareroot of variance. 1. TRUE 2.FALSE 3. TRUE 4. FALSE 5. FALSE 6. TRUE 7. FALSE 8. TRUE V. Assignment Given the data below, find the individual range, mean deviation and the standard deviation of the scores of the three students in their Mathematics quizzes. Determine which student has more consistent scores. VI. Remarks Prepared By: Junila A. Tejada Teacher Applicant
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