Formula Stat
Module 6: Measures of Variability, Skewness and Kurtosis | Ungrouped Data: VARIABILITY | | Meaning | Lesson | | Formula | Legend | Meaning | NOTE: | VARIABILITY(Four measures of Variability) | Measures of the average distance of each observation from the center of the distribution. | Range(R) | | R=Hv-Lv | Hv- Highest valueLv- Lowest value | Difference between hv and lv in data set. | | | | Variance | population (δ2) |
=∑(x-x)2N
| x – classmarkx –meanN - population | Average squared deviation from the mean. | | | | | sample(s2) | =∑(x-x)2n-1 | x – classmarkx –meann - sample | | | | | Standard Deviation | population (δ) |
=∑(x-x)2N
| | is square root of the average deviation from the mean, or simply the square root of the variance. | Square root lang yung result ng variance | | | | sample(s) | =∑(x-x)2n-1 | | | | Grouped Data: VARIABILITY | | Standard Deviation | population (δ) |
=∑f(x-x)2N
| f -frequency | | Note:‘pag mag-cocompute ng grouped data dapat lagging kasama ang frequency(number of observation). | | | Sample(s) | =∑f(x-x)2n-1 | f –frequency | | | Ungrouped Data: SHAPE OF DISTRIBUTION | Shape of Distribution | Skewness(SK) | | =m3m2m2Where:m2= ∑(x-x)2nm3= ∑(x-x)3n
SK=∑(x-x)3n∑(x-x)2n∑(x-x)2n | m-moment | Degree of symmetry or asymmetry of the distribution | | | Kurtosis(Ku) | | = m4m22-3Where:m4= ∑(x-x)4nKU=∑(x-x)4n∑(x-x)2n2-3 | | Refers to the peakedness or flatness of a distribution | - requires 4th moment- 3 is the normal distribution for kurtosis | Grouped Data | | Skewness(SK) | | =m3m2m2Where:m2= ∑(x-x)2nm3= ∑(x-x)3n
SK=∑f(x-x)3n∑f(x-x)2n∑f(x-x)2n | | | Note:‘pag mag-cocompute ng grouped data dapat lagging kasama ang frequency(number of observation). | | Interpretation:If SK = 0, distribution is normal relative to the center. Equal 0If SK < 0, distribution is skewed to the left. Less than 0If SK > 0, distribution is skewed to the right. Greater than 0 | |
=∑(x-x)2N
| x – classmarkx –meanN - population | Average squared deviation from the mean. | | | | | sample(s2) | =∑(x-x)2n-1 | x – classmarkx –meann - sample | | | | | Standard Deviation | population (δ) |
=∑(x-x)2N
| | is square root of the average deviation from the mean, or simply the square root of the variance. | Square root lang yung result ng variance | | | | sample(s) | =∑(x-x)2n-1 | | | | Grouped Data: VARIABILITY | | Standard Deviation | population (δ) |
=∑f(x-x)2N
| f -frequency | | Note:‘pag mag-cocompute ng grouped data dapat lagging kasama ang frequency(number of observation). | | | Sample(s) | =∑f(x-x)2n-1 | f –frequency | | | Ungrouped Data: SHAPE OF DISTRIBUTION | Shape of Distribution | Skewness(SK) | | =m3m2m2Where:m2= ∑(x-x)2nm3= ∑(x-x)3n
SK=∑(x-x)3n∑(x-x)2n∑(x-x)2n | m-moment | Degree of symmetry or asymmetry of the distribution | | | Kurtosis(Ku) | | = m4m22-3Where:m4= ∑(x-x)4nKU=∑(x-x)4n∑(x-x)2n2-3 | | Refers to the peakedness or flatness of a distribution | - requires 4th moment- 3 is the normal distribution for kurtosis | Grouped Data | | Skewness(SK) | | =m3m2m2Where:m2= ∑(x-x)2nm3= ∑(x-x)3n
SK=∑f(x-x)3n∑f(x-x)2n∑f(x-x)2n | | | Note:‘pag mag-cocompute ng grouped data dapat lagging kasama ang frequency(number of observation). | | Interpretation:If SK = 0, distribution is normal relative to the center. Equal 0If SK < 0, distribution is skewed to the left. Less than 0If SK > 0, distribution is skewed to the right. Greater than 0 | |