OBJECTIVESThe learners are expected to:a. Calculate the Standard   Deviation of a given set of   data.b. Calculate the Var...
STANDARD DEVIATION is a special form of average deviation from the mean. is the positive square root of the arithmetic m...
STANDARD DEVIATION is considered as the most reliable measure of variability. is affected by the individual values or it...
Standard Deviation for   Ungrouped Data
How to Calculate the  Standard Deviation for     Ungrouped Data1. Find the Mean.2. Calculate the difference   between each...
How to Calculate the   Standard Deviation for      Ungrouped Data4. Add up all the squares of the    difference between ea...
Find the Standard       Deviation    35            73    35            11    35            49    35            35    35   ...
Find the Standard         Deviationx    x-ẋ   (x-ẋ)2   x    x-ẋ   (x-ẋ)235   0       0      73   38    144435   0       0 ...
Find the Standard    Deviation
How to Calculate the   Standard Deviation for       Grouped Data1. Calculate the mean.2. Get the deviations by finding   t...
Find the Standard                              DeviationClass     F    Midpoint     FMp        _           _        _     ...
Find the Standard    Deviation
Characteristics of the     Standard Deviation1. The standard deviation is   affected by the value of every   observation.2...
Characteristics of the      Standard Deviation3. It has a definite mathematical     meaning and is perfectly     adapted t...
Characteristics of the      Standard Deviation5. The standard deviation is the    unit customarily used in    defining are...
VARIANCE is the square of the standard deviation.    In short, having obtained the value of the standard deviation, you c...
VARIANCE   It follows then that similarprocess will be observed incalculating both standarddeviation and variance. It ison...
Variance for Ungrouped         Data
How to Calculate theVariance for Ungrouped Data1. Find the Mean.2. Calculate the difference   between each score and the  ...
How to Calculate theVariance for Ungrouped Data4. Add up all the squares of the    difference between each    score and th...
Find the Variance    35           73    35           11    35           49    35           35    35           15    35    ...
Find the Variancex    x-ẋ   (x-ẋ)2   x    x-ẋ   (x-ẋ)235   0       0      73   38    144435   0       0      11   -24   57...
Find the Variance
Variance for Grouped Data
How to Calculate the Variance for Grouped Data1. Calculate the mean.2. Get the deviations by finding   the difference of e...
Find the VarianceClass     F    Midpoint     FMp        _           _        _            _Limits   (2)     (3)         (4...
Find the Variance
Standard Deviation and Variance
Standard Deviation and Variance
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Standard Deviation and Variance

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Standard Deviation and Variance

  1. 1. OBJECTIVESThe learners are expected to:a. Calculate the Standard Deviation of a given set of data.b. Calculate the Variance of a given set of data.
  2. 2. STANDARD DEVIATION is a special form of average deviation from the mean. is the positive square root of the arithmetic mean of the squared deviations from the mean of the distribution.
  3. 3. STANDARD DEVIATION is considered as the most reliable measure of variability. is affected by the individual values or items in the distribution.
  4. 4. Standard Deviation for Ungrouped Data
  5. 5. How to Calculate the Standard Deviation for Ungrouped Data1. Find the Mean.2. Calculate the difference between each score and the mean.3. Square the difference between each score and the mean.
  6. 6. How to Calculate the Standard Deviation for Ungrouped Data4. Add up all the squares of the difference between each score and the mean.5. Divide the obtained sum by n – 1.6. Extract the positive square root of the obtained quotient.
  7. 7. Find the Standard Deviation 35 73 35 11 35 49 35 35 35 15 35 27 210 210Mean= 35 Mean= 35
  8. 8. Find the Standard Deviationx x-ẋ (x-ẋ)2 x x-ẋ (x-ẋ)235 0 0 73 38 144435 0 0 11 -24 57635 0 0 49 14 19635 0 0 35 0 035 0 0 15 -20 40035 0 0 27 -8 64∑(x-ẋ)2 0 ∑(x-ẋ)2 2680
  9. 9. Find the Standard Deviation
  10. 10. How to Calculate the Standard Deviation for Grouped Data1. Calculate the mean.2. Get the deviations by finding the difference of each midpoint from the mean.3. Square the deviations and find its summation.4. Substitute in the formula.
  11. 11. Find the Standard DeviationClass F Midpoint FMp _ _ _ _Limits (2) (3) (4) X Mp - X (Mp-X)2 f( Mp-X)2 (1)28-29 4 28.5 114.0 20.14 8.36 69.89 279.5626-27 9 26.5 238.5 20.14 6.36 40.45 364.0524-25 12 24.5 294.0 20.14 4.36 19.01 228.1222-23 10 22.5 225.0 20.14 2.36 5.57 55.7020-21 17 20.5 348.5 20.14 0.36 0.13 2.2118-19 20 18.5 370.0 20.14 -1.64 2.69 53.8016-17 14 16.5 231.0 20.14 -3.64 13.25 185.5014-15 9 14.5 130.5 20.14 -5.64 31.81 286.2912-13 5 12.5 62.5 20.14 -7.64 58.37 291.85 N= ∑fMp= ∑(Mp-X)2= 100 2,014.0 1,747.08
  12. 12. Find the Standard Deviation
  13. 13. Characteristics of the Standard Deviation1. The standard deviation is affected by the value of every observation.2. The process of squaring the deviations before adding avoids the algebraic fallacy of disregarding the signs.
  14. 14. Characteristics of the Standard Deviation3. It has a definite mathematical meaning and is perfectly adapted to algebraic treatment.4. It is, in general, less affected by fluctuations of sampling than the other measures of dispersion.
  15. 15. Characteristics of the Standard Deviation5. The standard deviation is the unit customarily used in defining areas under the normal curve of error. It has, thus, great practical utility in sampling and statistical inference.
  16. 16. VARIANCE is the square of the standard deviation. In short, having obtained the value of the standard deviation, you can already determine the value of the variance.
  17. 17. VARIANCE It follows then that similarprocess will be observed incalculating both standarddeviation and variance. It isonly the square root symbolthat makes standard deviationdifferent from variance.
  18. 18. Variance for Ungrouped Data
  19. 19. How to Calculate theVariance for Ungrouped Data1. Find the Mean.2. Calculate the difference between each score and the mean.3. Square the difference between each score and the mean.
  20. 20. How to Calculate theVariance for Ungrouped Data4. Add up all the squares of the difference between each score and the mean.5. Divide the obtained sum by n – 1.
  21. 21. Find the Variance 35 73 35 11 35 49 35 35 35 15 35 27 210 210Mean= 35 Mean= 35
  22. 22. Find the Variancex x-ẋ (x-ẋ)2 x x-ẋ (x-ẋ)235 0 0 73 38 144435 0 0 11 -24 57635 0 0 49 14 19635 0 0 35 0 035 0 0 15 -20 40035 0 0 27 -8 64∑(x-ẋ)2 0 ∑(x-ẋ)2 2680
  23. 23. Find the Variance
  24. 24. Variance for Grouped Data
  25. 25. How to Calculate the Variance for Grouped Data1. Calculate the mean.2. Get the deviations by finding the difference of each midpoint from the mean.3. Square the deviations and find its summation.4. Substitute in the formula.
  26. 26. Find the VarianceClass F Midpoint FMp _ _ _ _Limits (2) (3) (4) X Mp - X (Mp-X)2 f( Mp-X)2 (1)28-29 4 28.5 114.0 20.14 8.36 69.89 279.5626-27 9 26.5 238.5 20.14 6.36 40.45 364.0524-25 12 24.5 294.0 20.14 4.36 19.01 228.1222-23 10 22.5 225.0 20.14 2.36 5.57 55.7020-21 17 20.5 348.5 20.14 0.36 0.13 2.2118-19 20 18.5 370.0 20.14 -1.64 2.69 53.8016-17 14 16.5 231.0 20.14 -3.64 13.25 185.5014-15 9 14.5 130.5 20.14 -5.64 31.81 286.2912-13 5 12.5 62.5 20.14 -7.64 58.37 291.85 N= ∑fMp= ∑(Mp-X)2= 100 2,014.0 1,747.08
  27. 27. Find the Variance
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