Lesson 5 Measures of variability Flashcards
- Are measures of the average distance of each observation from the center of the distribution.
- They measure the homogeneity or heterogeneity of a particular group
Measures of variability or dispersion
A small measure of variability would indicate that the data are:
- clustered closely around the mean
- more homogeneous
- less variable
- more consistent
- more uniformly distributed.
Measures of Variability or Dispersion
Range (R)
Mean Absolute Deviation (MAD)
Variance
Standard Deviation
Coefficient of Variation (cv)
This is the simplest but the most unreliable measure of variability since it uses only two values in the distribution
Range (R)
Disadvantages of Range
- For a very large sample, it is an unstable descriptive measure of dispersion.
- Since only two values are used in the computation, the range is an unreliable measure of dispersion.
- The range of two sets of data composed of different numbers of samples are not directly comparable
is the simplest measure of variability that takes into account all data in the distribution
Mean Absolute Deviation (MAD)
Disadvantages of MAD
- Since the mean is used in its computations, then it is also greatly affected by extreme values
- Its use in further statistical computation is very limited
- It is not amenable to algebraic manipulation because of the use of absolute values.
are both reliable measures of variability or spread of the distribution
However, we cannot use them in comparing two sets of data of different units
SD and Variance
is the ratio of the standard deviation to the mean.
It is used to compare the variability of two or more sets of data even when they are expressed in different units of measurement.
Coefficient of variation (cv)
is the square root of the average deviation from the mean, or simply the square root of the variance.
Standard Deviation
is the average of the squares of the differences between the individual (observed) and the expected value
Variance
is a distribution with a bell-shaped appearance.
Normal distribution
refers to the degree of symmetry or asymmetry of a distribution
Skewness
If a distribution is skewed to the left
mean is less than its median
(mean < median)
negatively skewed
If a distribution is skewed to the right
mean is greater than its median
(mean > median)
positively skewed