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# Measures of Central Tendency

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### Measures of Central Tendency

1. 1. A Detailed Lesson Plan in Mathematics 7 – Measures ofCentral Tendency of Ungrouped Data I. OBJECTIVES After 45 minutes of Discussion about “Measures of Central Tendency of Ungrouped Data” 90% of the Grade 7 students with 95% level of understanding should be able to: 1. define each of the three measures of centraltendency. 2. appreciate the significance of the measures of centraltendency. 3. calculate each of the three measures of central tendency. II. SUBJECT MATTER TOPIC:Measures of Central Tendency of the Ungrouped Data MATERIALS: visual Aids – cartolina, numbers REFERENCES: Mathematics 7, Learner’sModule, pp. 491-496 SKILLS: Computing and Analyzing VALUES INTEGRATION:Associate the measures of central tendency in the real life situation. III. PROCEDURE (Inductive) TEACHER’S ACTIVITY STUDENTS’ ACTIVITY A. Preparation Good morning class. Class, let’s all stand and pray, Let’s bow our heads to feel the presence of the Lord. In the name of the father, the son, the holy spirit. AMEN. Lord help us, Good morning ma’am. Lord help us to, Add our Patience Subtract our Sins Multiply our Blessings And Divide our time to serve you. AMEN…
2. 2. While the class monitors checking the attendance, Kindly pick up the pieces of paper under your chair. So, we have a perfect attendance,right class? - okay, very good!! *Review of the past lesson Last meeting we discussed about the Organizing data. So let’s have a short review. What is organizing data? Yes,__________? Exactly! What are the different forms used in organizing data? Yes,_________? Very good! *Motivation Class, I prepared something under your chair. Kindly get and paste it on the blackboard. The data are 85,80,88,83,87,89,84,80,94,93,95,97,96,99,98 and 90. Call a student to arrange the numbers from least to greatest. Class, what do you observe with the data? Yes,_____________? That’s a great answer! Class if am I going to use these data 80,80,83,84,85,87,88,89,90 and 94 as the math grades of the 10 students. Do you know that these data can also be summarized into a single number or single data? B. Presentation So be with me this morning class, as I discuss to you about “Measures of central Tendency of Ungrouped Data”. Everybody read! - Yes,ma’am Organizing Data is the sorting, presenting and arranging of collected information. 1. Textual form 2. Tabular form 3. Graphical form The student paste the numbers on the board 80,80,83,84,85,87,88,89,90,93,94,95,96,97,98,99. The Data given are all numbers and it is arranged in order. - No, ma’am “Measures of central Tendency of Ungrouped Data”
3. 3. Okay, class listen carefully because after my discussion you will be asked to define each of the three measures of centraltendency, appreciate the significance of the measures of centraltendency in associating it into the real life situation and lastly, you will be asked to calculate each of the three measures of central tendency. Am I understood class? C. Comparison and Abstraction Class there are three measures of central tendency, first one is the mean. Mean- or “average”,is the most commonly used measure of central tendency. It is defined as the sum of all the data scores divided by the number of scores. 𝑀𝑒𝑎𝑛 = 𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝐷𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠 For example: The grade of grade 7 student in math were as follows: 80,81,83,84, So from the formula given, let us now try to analyze and then substitute the given values to the given formula. 𝑀𝑒𝑎𝑛 = 𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝐷𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠 = 80 + 81 + 83 + 84 4 = 328 4 = 82 Hence,the mean grade of the ten students is 82. Let’s have another example. The five players of basketball team have the scores of 10,15,20,10, and 25. - Yes,ma’am
4. 4. Who can answer the given example by applying the formula? Yes,____________? Very Good! Therefore,the mean score of the five players of basketball is 16. Do you understand class on how to find the mean of the given data? Is there any question? Okay let us proceed to the second measure of central tendency. Median- it is the middle value. To find the median, we have to follow the rule. Arrange the data in order, from least to greatest. First example: 10,15,20,10,25 Solution: Apply the rule. Arrange the data in order, from least to greatest. Then find the middle value. 10,10,15,20,25 Median = 15 2) 28, 35,15,12,18. What is the median? 3) 80,80,83,84,85,87,88,89,90,94. What is the median? Why? 𝑀𝑒𝑎𝑛 = 𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝐷𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠 = 10+10+15+20+25 5 = 80 5 = 16 - Yes,ma’am - None, ma’am 12,15,18,28,35 Ma’am the median is 18. -None, Ma’am There is no middle value ma’am.
5. 5. Okay class, since the middle point falls hallway between 85 and 87, so in order to get the median, we need get the mean of these two values. Median = 85+87 2 = 172 2 = 86 Therefore,the median of the given data is 86. So do you understand class on how to find the median of a set of data? Is there any question? Okay let us proceed to the next measure of central tendency. Mode- it is the value that occurs the most often in the data set. To find the mode for a set of data just select the value that appears most often. Always remember, if the given data set doesn’t have a mode, don’t write zero mode just write no mode. And also, don’t forget the Rule. First example: Using the same data. 80,80,83,84,85,87,88,89,90,94. Which value appears the most? Since 80 is the value that appears the most. Therefore,80 is the mode. 2) Find the mode of the data set 21,23,25,26,24,27,21 Since 21 is the value that appears the most. Therefore,21 is the mode. Class is everything clear? Do you have any question? - Yes,ma’am - No, ma’am 80 ma’am 21,21,23,24,25,26,27 21 is the mode ma’am - Yes, ma’am - None, ma’am
6. 6. 3) 24,23,23,22,22,21 What is the mode? So if there are 2 modes, we call them as bimodal. If there are 3 modes, we call them as trimodal if more than 3 we call them multimodal. D. Generalization Okay, again class. What are the three measures of central tendency? Yes,___________? What is the formula of Mean? - Very Good! What is the rule in finding the median and mode? Yes, __________? Precisely! What will you write if the the given data doesn’t have a mode? Yes,_________? Exactly! E. Application Okay, Let’s now have a drill. Group yourself into 9. You have five minutes to collect data from your group mates. Ask the following questions and record the data. 1. What is your shoe size? a) find the mean. b) find the median. c) find the mode. 2. What is your age? a) find the mean. b) find the median. c) find the mode. Ma’am there are 2 numbers that appear the most, these are 22 &23. Mean, Median, Mode 𝑀𝑒𝑎𝑛 = 𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑑𝑎𝑡𝑎 𝐷𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑐𝑜𝑟𝑒𝑠 Arrange the data in order. No mode. (Students Answered) (Students Answered)
7. 7. IV. EVALUATION Directions: The data below shows the score of a student in the Monthly Examination. Analyze the given data and answer the question below. 85,80,88,83,87,89,84,80,94,93,95,97,96,99,98,90 a. What score appears to be the median? How many students fail below that score? b. Which scores frequently appears? c. Calculate the mean, median and mode. 2. Appreciate the significance of the measures of centraltendency into reallife situation. Justify your answer. V. ASSIGNMENT Direction: In your one-half crosswise, find the mean, median and mode. 1. Twelve computer students were given a typing test and the times (in minutes) to compute the test were as follow: 8, 12, 15, 14, 19, 21, 24, & 38 Prepared By: Regina C. Cruz
8. 8. Mary the Queen College of Pampanga (Inc.) General Teaching Demonstration A Detailed Lesson Plan in Mathematics 7 Submitted by: Regina C. Cruz Student Teacher Submitted to: Mrs. Shirley M. Dabu Cooperating Teacher Date: February 10, 2017
9. 9. Mary the Queen College of Pampanga (Inc.) General Teaching Demonstration A Detailed Lesson Plan in Mathematics 7 Submitted by: Arlyn S. Paule Student Teacher Submitted to: Mr. Ray-an P. Ramos Cooperating Teacher Date: February 10, 2017
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