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### Measures of Variability of Grouped and Ungrouped Data

• 1.
• 2. Learning Competency: Calculates the measures of variability of grouped and ungrouped data.
• 3. Learning Objectives: 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.
• 5. SET A: 4, 10, 12, 20, 24 SET B: 12, 13, 14, 15, 16 Given the set of data, use your understanding on the measures of central tendency to find the following question: What is the mean of Set A? How about Set B? The mean is 14 The mean is 14
• 6. 4. Draw a number line of each of the Set and plot the data. SET A: 4, 10, 12, 20, 24 SET B: 12, 13, 14, 15, 16
• 7. Are you familiar with the term “measures of variability”?
• 8.
• 9. Your task: The students will arrange the shuffled letters by sequencing the clues indicated below the letter. The activity is for only 5 minutes. Once the time is done, the students will submit their work. Note:
• 10.
• 11. What did we do in our activity?
• 12.
• 13. What is the word for number 1? RANGE In order to find the spread of the scores of Mel, what did she discover? She subtract the lowest score from the highest score.
• 14. Mel has a raw score of 5, 6, 7, 8,9,10 in Math and a raw score of 3, 7, 8, 9, 10,11 in English R What will be the range of Mel scores in Math? In English? Math: 5 English: 8 Based on the range, which set has less spread? Math: 5
• 15. The formula for the range is also applicable to GROUPED data. Now, we will determine the highest score and the lowest score and find its upper and lower boundary. Simply subtract the highest to the lowest boundary which is: 22.5 – 10.5 = 12
• 16. What if the two sets of data have the same range? Is there other way to compute the spread of the data?
• 17.
• 18. What is the answer for the shuffled letter no. 2? MEAN DEVIATION What did Joy find first? What is the mean? 25 In subtracting the individual scores to the mean why it is important to get its absolute value?
• 19. In mean deviation, we are concerned with the distance of the individual scores from the mean Now we will add the difference of the x and the mean Then we will divide the sum by the number of terms. 40 4 = 10
• 20.
• 21. In the letter V, it indicates that it is a raw score, is data grouped or ungrouped? UNGROUPED DATA Let us focus on number 3, what is the word? VARIANCE What is the first step of Veronica in finding the spread of her scores?
• 22. 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. Now we will add the summation of the squared data Then we will divide the sum by the number of terms. 4 20 5=
• 23.
• 24. Let us focus on number 4, what is the word? STANDARD DEVIATION Standard deviation is the squareroot of variance.
• 25. Joanna has a raw score of 50, 52, 54, 56. Find the mean Create a table. Now we will add the summation of the squared data 20 Then we will divide the sum by the number of terms. 4 5= = = 2.24
• 26.
• 27. What is the word for number 5? VARIANCE What is the first step? find the class mark By adding the two interval and dividing it by the number of terms
• 29.
• 31. What do you think is difference of this variance from the variance presented earlier?
• 32.
• 33. Let us focus on the last number, what is the word? STANDARD DEVIATION Standard deviation is the squareroot of variance.
• 35. Measures of Variability The measures of variability allows us to know how spread our scores from the mean and from each other Always remember that the lesser the variability, the more consistent the scores and the data.
• 36. Measures of Variability of Ungrouped and Grouped Data Range Mean Deviation
• 37. Measures of Variability of Ungrouped and Grouped Data Variance (Ungrouped)
• 38. Measures of Variability of Ungrouped and Grouped Data Variance
• 39. Measures of Variability of Ungrouped and Grouped Data Standard Deviation (Ungrouped)
• 40. Measures of Variability of Ungrouped and Grouped Data Standard Deviation (Grouped)
• 42.
• 43. 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 10 minutes of the time. The class will be divided into two groups.
• 44.
• 45.
• 46. 1. Complete the table below and find the: 1.1 Standard Deviation 1.2 Variance 1.3 Range
• 47.
• 48. 2. Complete the table below and find the: 2.1 Variance 2.2 Standard deviation
• 49.
• 50. Learning Objectives: 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.
• 52. Class, write TRUE if the statement is true and FALSE if the statement is false. You have five 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.
• 53. Class, write TRUE if the statement is true and FALSE if the statement is false. You have five minutes to answer this quiz. 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.
• 54. Class, write TRUE if the statement is true and FALSE if the statement is false. You have five minutes to answer this quiz. 1. The measures of variability allows us to determine the spread of the data. TRUE 2. The greater the variability, the more consistent the scores. FALSE 3. In finding the range of ungrouped data, we will subtract the highest score to the lowest score. TRUE 4. In finding the range of the group data, we will subtract the highest class mark to the lowest class mark. FALSE
• 55. Class, write TRUE if the statement is true and FALSE if the statement is false. You have five minutes to answer this quiz. 5 . The first step in getting the variance of grouped data is to determine the class boundary. FALSE 6. In finding the mean deviation, it is important to get the absolute value of (x-mean). TRUE 7. In finding the variance, we need to square root the result of (x-mean). TRUE 8. Standard deviation is the squareroot of variance. TRUE
• 56. 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.
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