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THE AVERAGE DEVIATION

THE AVERAGE DEVIATION. While the range is based on the highest and lowest values in a distribution, average deviation is influenced by all the individual observation. It is the average amount by which any value in a distribution differs from the mean. EXAMPLE 1.

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THE AVERAGE DEVIATION

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  1. THE AVERAGE DEVIATION While the range is based on the highest and lowest values in a distribution, average deviation is influenced by all the individual observation. It is the average amount by which any value in a distribution differs from the mean.

  2. EXAMPLE 1 The distribution below consists of the ages of the 5 children of two families A and B. Family A  8, 11, 13, 15, 18 Family B  3, 7, 12, 17, 21

  3. The amount of difference of each value from the mean regardless of the algebraic sign is called the absolute deviation. For Family A, the mean is 13. For Family B, the mean is 12.

  4. Thus, The mean of these deviations is called the average deviation. Family B/3 -12/ = 9 /7 -12/ = 5 /12 - 12/ = 0 /17 - 12/ = 5 /21 - 12/ = 9 Family A/8 -13/ = 5 /11 -13/ = 2 /13 - 13/ = 0 /15 - 13/ = 2 /18 - 13/ = 5

  5. For Family AAve. Deviation = 5 + 2 + 0 + 2 + 5 5 = 14/5 or 2.8 For Family BAve. Deviation = 9 + 5 + 0 + 5 + 9 5 = 28/5 or 5.6

  6. A.D. = /x -x/ n In general, average deviation is computed as

  7. The size of the average deviation indicates the spread or variability of the observations. A large average deviation means the observations are widely dispersed about the mean as the ages in Family B. A small averagedeviation means that the observations are quite close to the mean as the ages in Family A.

  8. S.D. = (x -x)2 n THE STANDARD DEVIATION The most commonly used measure of spread is the standard deviation or S.D. Like the average deviation, it is influenced by every value in the distribution. It is computed as

  9. Example A Consider Rina’s quizzes in Filipino78, 65, 81, 85, 75, 72

  10. Study the following steps in computing for Standard Deviation (S.D.) 1.) Find the mean of the distribution. x = 456 or 76 6

  11. 2.) Find the difference between every item and the mean. (Deviation) 78 - 76 = 265 - 76 = -1181 - 76 = 585 - 76 = 975 - 76 = -172 - 76 = -4

  12. 3.) Square each difference. (Squared Deviation) 22 = 4(-11)2 = 12152 = 2592 = 81(-1)2 = 1(-4)2 = 16

  13. 4.) Get the sum of the squares and divide by the number of items. 248 or 41.33 6

  14. S.D. =  41.33 = 6.43 5.) Find the square root of the quotient in no. 4. This is the Standard Deviation (S.D.)

  15. Unlike in average deviation, standard deviation takes into account the positive and the negative signs of the deviations. Since the sum of the deviations will always equal to zero, the deviations are squared and the squares are added.

  16. Example B Calculate the S.D. for Rina’s score in Advanced Algebra : 70, 81, 78, 68, 73, 80

  17. Let us organize the computation in this manner.

  18. x = x n To compute for the Mean = 450 or 75 6

  19. = 148 6 S.D. = (x -x)2 n =  24.67 Substituting from the formula to solve for the Standard Deviation (S.D.) = 4.97

  20. The smaller standard deviation obtained in Example B (S.D. = 4.97) than that obtained in Example A (S.D. = 6.43) indicates that Rina performs consistently better in Advanced Algebra than in Filipino. The End ...

  21. SEATWORK Instruction :Get the mean in the following samples scores and find the standard deviation. Which school performs better in the entrance examinations ? Why ? Results of the entrance examinations of the top 10 students of St. Agnes Academy : 91, 86, 91, 89, 90, 88, 89, 85, 86, 85 Zamboanga Veritas School : 82, 88, 88, 85, 94, 86, 84, 92, 90, 81

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