MATH 8 Q1 LESSON 1_MEAN, MEDIAN AND MODE

Presentation on Mean, Median and Mode

1. Sharpen your minds, - It’s Math time

2. Σ N Measures of Central Tendency of Ungrouped Data Math 8, Quarter 1, Lesson 1

3. LESSON OBJECTIVES: By the end of the lesson, the learners are expected to: 1. define measures of the central tendency of ungrouped data; 2. compute the mean, median and mode of ungrouped data; and 3. generate insights from statistical data using measures of central tendency.

4. 1 day

5. SHORT REVIEW

6. Activity 1: Do You Remember? I dentify whether the following data is qualitative or quantitative

7. 1. general average QUALITATIVE QUANTITATIVE

8. 2. civil status QUALITATIVE QUANTITATIVE

9. 3. annual income QUALITATIVE QUANTITATIVE

10. 4. years in school QUALITATIVE QUANTITATIVE

11. 5. educational attainment QUALITATIVE QUANTITATIVE

12. 6. skin color QUALITATIVE QUANTITATIVE

13. 7. age QUALITATIVE QUANTITATIVE

14. 8. number of children QUALITATIVE QUANTITATIVE

15. 9. weight QUALITATIVE QUANTITATIVE

16. 10. social class QUALITATIVE QUANTITATIVE

17. LESSON PURPOSE

18. Activity 2: Meet Me in the Middle Analyze the two number lines and answer the questions that follow

19. Question: 1. What is the middle value of the indicated numbers in the number line on the left? 5

20. Question: 2. What is the middle value of the indicated numbers in the number line on the left? 5

21. Question: 3. How were you able to find the answer for each given number line? 5 5

22. UNLOCKING CONTENT VOCABULARY

23. Ungouped data vs grouped data UNGROUPED DATA refers to raw data that is listed individually, without being organized into categories or intervals. Each value stands alone and is not part of a frequency distribution. Example: Test scores of students: 78, 85, 90, 92, 85, 88, 90, 78, 82, 76, 79, 95, 90, 88 GROUPED DATA is a statistical data set in which the values are organized into groups (classes) instead of being listed individually. Example: Test scores of students:

24. 1 M EAN is the sum of the data values divided by the number of values. This is also referred to as the average . The mean is the balance point of a distribution. 2 Put on your thinking hats and solve these word problems! 3 Measures of Central Tendency are a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location. M EDIAN is the number that falls in the middle position once the data has been organized from smallest to largest or largest to smallest. M ODE is the value that appears most frequently in the set of data.

25. Measures of Central Tendency 3Ms ean edian ode M 3Ms 3Ms 3Ms 3Ms 3Ms 3Ms

26. 2 day

27. SHORT REVIEW

28. 1. What is the mean of a set of numbers? A. The number that appears most often B. The middle number when arranged in order C. The sum of all values divided by the number of values D. The highest number in the data set

29. 2. What is the median of a data set? A. The average of the data B. The difference between the highest and lowest numbers C. The number that appears most often D. The middle value when data is arranged in order

30. 3. What does the mode represent in a set of numbers? A. The total sum B. The number that occurs most frequently C. The difference between the highest and lowest numbers D. The median of two values

31. 4. MEAN, MEDIAN AND MODE ARE CALLED _______________ A. Measures of position B. Measures of variability C. Measures of central tendency D. None of the above

32. EXPLICITATION

33. FINDING THE MEAN

34. FINDING THE MEAN In finding the mean of ungrouped data, we find the sum of values (x) divided by the number of values in the data set represented by N. We use the formula:     x̄ = mean = 𝑠𝑢𝑚 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 𝑁 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠   or   Note: The symbol Σ (sigma) is a Greek letter used to indicate summation.

35. FINDING THE MEAN Find the mean of: 8, 12, 10, 15, 5 Step 1: Add the values 8 + 12 + 10 + 15 + 5 Step 2: Count the number of values There are 5 numbers. Step 3: Divide the sum by the number of values 10   (the mean is 10) = 50

36. FINDING THE MEAN Scores of 10 students in a Periodic Test: 28, 32, 24, 30, 41, 18, 12, 14, 21, 28 Mean = 28+32+24+30+41+18+12+14+21+28 10 = 248 10 = 24.8 or 25 (the mean is 24.8 or 25)

37. FINDING THE MEDIAN

38. In finding the median of ungrouped data, we arranged the values of the data set in either increasing or decreasing order and find the middle score . If there are two middle values, we add those and divide it by 2 or where 𝑥 1 𝑎𝑛𝑑 𝑥 2 are the two middle values.   FINDING THE MEDIAN

39. FINDING THE MEDIAN Find the median of: 8, 12, 10, 15, 5 Step 1: Arrange the numbers in order 5, 8, 10, 12, 15 Step 2: Find the middle value 5, 8, 10, 12, 15 The median is 10

40. FINDING THE MEDIAN Scores of 10 students in a Periodic Test: 28, 32, 24, 30, 41, 18, 12, 14, 21, 28 12, 14, 18, 21, 24, 28, 28, 30, 32, 41 There are two middle values, so we add those and divide by 2 Median =   =   = 26 (the median is 26)

41. FINDING THE mode

42. In finding the mode , select the value that appears most often in the data set. If two or more values appear the same number of times, then each of the values is a mode. However, if all scores appear the same number of times, then the set of data has no mode. FINDING THE MODE

43. NO MODE , because the scores appear the same number of times FINDING THE MODE Find the mode of: 8, 12, 10, 15, 5 Scores of 10 students in a Periodic Test: 28, 32, 24, 30, 41, 18, 12, 14, 21, 28 The mode is 28 , because it appears twice. 9 and 15 are the modes, why? Find the mode of: 9, 15, 10, 15, 5, 9, 15, 10, 9, 5

44. SUMMARY GIVEN MEAN MEDIAN MODE 8, 12, 10, 15, 5 10 10 NONE 28, 32, 24, 30, 41, 18, 12, 14, 21, 28 24.8 26 28 Remember: The mean, median and mode are always within the given data. This means they will never be outside the smallest or largest number in the set. All three measures help describe the “center” of the data, but they may be different from each other.

45. GENERALIZATION

46. 3 day

47. SHORT REVIEW

48. Mean means average (2x) You add, then divide (2x) Median is in the middle (2x) Mode means most (2x) MEAN, MEDIAN & MODE SONG

49. WORKED EXAMPLES

50. Example 1: The shoe sizes of the members of the basketball team Liliw Lakers are 7, 9, 11, 8, 8, 8, 7, 8, 9, 10, 8. Compute for the measures of central tendencies. A. MEAN Hence, the average shoe size of the members of the basketball team is 8.45. B. MEDIAN By rearranging the values in increasing order: 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 11 since the middle value is the median, then the median is 8 . C. MODE Since 8 is the most repeated value in the data set, then the mode is 8. The most occurring shoe size of the player is 8.      

51. Example 2: Teacher Abigail recorded the number of spelling errors made by her 8 students during the test, 6, 5, 4, 6, 2, 0, 5, 1. Compute for the measures of central tendencies. A. MEAN Hence, the average number of spelling errors is 3.63. B. MEDIAN Let’s try rearranging the values in decreasing order: 6, 6, 5, 5, 4, 2, 1, 0 since there are two middle values, we add them and divide it by two 5 + 4 = 9 ÷ 2 = 4.5, then the median is 4.5 C. MODE Since 5 and 6 occur the same number of times in the data set, then the mode is both 5 and 6. The data set is bimodal. Most students commit 5 or 6 spelling errors.      

52. Example 3: Six members of the class list the number of brothers and sisters they have. These six numbers, in ascending order are 2, 0, 0, 4, 2, and 4. Compute for the measures of central tendencies. A. MEAN Hence, the average number of brothers and sisters is 2. B. MEDIAN By rearranging the values in increasing order: 0, 0, 2, 2, 4, 4 since there are two middle values, we add them and divide it by two 2 + 2 = 4 ÷ 2 = 2, then the median is 2 C. MODE Since all values occur the same number of times, then the data set has no mode.      

53. Example 4: The weights in kilograms of the runners in the annual district level marathon are the following: 90.7, 89.5, 93.4, 92.1, 82.6, 92.5, 94.4, 89.5, 86.7, 90.4, 94.4, 97.1, 89.5 Find the mean, median and mode. A. MEAN Hence, the average weight of runners is 90.98 kg B. MEDIAN By rearranging the values in increasing order: 82.6, 86.7, 89.5, 89.5, 89.5, 90.4, 90.7, 92.1, 92.5, 93.4, 94.4, 94.4, 97.1 since the middle value is the median, the median is 90.7 C. MODE Since 89.5 is the most repeated value in the data set, then the mode is 89.5 The most occurring weight of the runners is 89.5 kg.      

54. Mean means average (2x) You add, then divide (2x) Median is in the middle (2x) Mode means most (2x) MEAN, MEDIAN & MODE SONG Let’s sing again

55. 4 day

56. LESSON ACTIVITY

57. Mistakes help us learn— let’s be brave and do our best in math!

58. GIVEN MEAN MEDIAN MODE 1. The number of incorrect answers on a true-or-false test of your 15 classmates were recorded by your teachers as follows: 2, 1, 3, 0, 1, 3, 6, 0, 3, 3, 5, 2, 1, 4 and 2. 2. The number of building permits issued by your municipality last month were 4, 7, 0, 11, 4, 1, 15, 3, 5, 8, and 7. 3. An experiment was conducted for a random sample of 9 subjects. A stimulant was applied to each subject and the recorded reaction time in seconds are 2.5, 3.6, 3.1, 4.3, 2.9, 2.3, 2.6, 4.1 and 3.4. 4. The scores of 9 students in a 100-item test are 67, 70, 49, 95, 40, 97, 62, 54, and 42. Find the measures of central tendencies

59. 5. A set of data consists of five numbers. The mode is 2. The median is 3. The mean is 4. The difference between the largest and smallest number is 6. What are the five numbers?

60. GIVEN MEAN MEDIAN MODE 1. The number of incorrect answers on a true-or-false test of your 15 classmates were recorded by your teachers as follows: 2, 1, 3, 0, 1, 3, 6, 0, 3, 3, 5, 2, 1, 4 and 2. 2.4 2 3 2. The number of building permits issued by your municipality last month were 4, 7, 0, 11, 4, 1, 15, 3, 5, 8, and 7. 5.91 5 4, 7 3. An experiment was conducted for a random sample of 9 subjects. A stimulant was applied to each subject and the recorded reaction time in seconds are 2.5, 3.6, 3.1, 4.3, 2.9, 2.3, 2.6, 4.1 and 3.4. 3.2 3.1 NONE 4. The scores of 9 students in a 100-item test are 67, 70, 49, 95, 40, 97, 62, 54, and 42. 64 62 NONE Find the measures of central tendencies ANSWER KEY

61. 5. A set of data consists of five numbers. The mode is 2. The median is 3. The mean is 4. The difference between the largest and smallest number is 6. What are the five numbers? 2, 2, 3, 5, 8 ANSWER KEY

62. GREAT JOB!

63. MAKING GENERALIZATIONS

64. Learners’ Takeaways and Reflection on Learning Activity 4: Closing the Loop! Instruction: answer the following questions. 1. What are the key concepts of our lesson? 2. Which part of the lesson is the easiest for you? Why? 3. Which part of the lesson is the hardest for you? Why? 4. How are we as a class today?

65. 5 day

66. FORMATIVE ASSESSMENT

67. Activity 5: Let’s Solve It! Instruction: analyze and answer the question that follows. Questions: Based on the table, what is the mean, median and mode heat index? What does each measure of central tendency imply?

68. Mean, Median, and Mode Quiz 1. What is the mean of the numbers 3, 5, 7, 9, 11? A. 7 B. 9 C. 5 D. 11 2. What is the median of the numbers 2, 7, 4, 9, 5? A. 4 B. 5 C. 6 D. 7 3. What is the mode of the numbers 6, 1, 6, 3, 2, 6? A. 3 B. 6 C. 1 D. 2 4. What is the mean of the numbers 8, 10, 12, 14? A. 12 B. 10 C. 11 D. 9 5. Which of the following has no mode? A. 3, 3, 6, 6, 9 B. 4, 4, 4, 5, 6 C. 2, 3, 4, 5, 6 D. 1, 1, 2, 2, 3 6. What is the median of the numbers 11, 8, 15, 9, 10? A. 10 B. 11 C. 9 D. 8 7. If the mean of 4 numbers is 10, what is their total sum? A. 10 B. 40 C. 14 D. 4 8. Which of the following statements is true? A. The mean is always one of the numbers in the data set. B. The mode is always the middle number. C. The median is the number that appears most often. D. The mean is the average of the numbers. 9. What is the mode of the numbers 5, 6, 6, 7, 8, 8? A. 5 B. 6 and 8 C. 7 D. No mode 10. What is the median of the numbers 4, 6, 8, 10, 12, 14? A. 10 B. 8 C. 9 D. 11

69. Answer key Activity 5: Let’s Solve It! Mean, Median, and Mode Quiz

70. Have a great day ahead THANK YOU!

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