indicates the extent to which the individual items in a series are scattered about an average
Measures of Dispersion
a point at which certain percentage of the observations lie below the indicated point when all the observations are ranked in descending order
percentile of a distribution
what are the Measures of Absolute Dispersion
Range, Standard Deviation, Variance
what are the Measures of Relative
Dispersion
Coefficient of Variation, Standard Score
expressed in the units of the original observations
Cannot be used to compare variations of two data sets when the averages of these data sets differ a lot in value or when observations differ in units of measurements
Measures of Absolute Dispersion
Distance covered by the scores in a distribution, from the smallest score to the largest score
Most obvious way to describe how spread out the scores are
Range
what is the formula for range
Highest – Lowest
state characteristics of range
- uses only extreme values
*outlier can greatly alter the value
*cannot be approximated from open-ended frequency distributions
*fails to communicate any information about the clustering or the lack of clustering of the values between the extremes - outlier can greatly alter the value
- cannot be approximated from open-ended frequency distributions
- unreliable when computed from frequency distribution table with gaps or zero frequencies
equals the mean of the squared deviations
variance
uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and the mean
standard deviation
give characteristics of standard deviations
- Affected by the value of each observation
- Cannot be computed from an open-ended
distribution - If each observation of a set of data is transformed to a new set by addition/subtraction of a constant, the SD of a
new set of data is the same as the SD of the
original data set - If a set of data is transformed to a new set by multiplying/dividing each observation by a constant “c”, the SD of the new data set is equal to the SD of the original data set
multiplied/divided by “c”
when do u use population standard deviation
- You have the entire population
- You have a sample of a larger population, but only interested in a sample and you do not wish to generalize your findings to the population
when do u use sample standard deviation
You have a sample, but wish to make a statement about the population SD, from which the sample is drawn
unitless; used when one wishes to compare the scatter of one distribution with another distribution
Measures of Relative Dispersion
- ratio of the SD to the mean
- usually expressed in percentage
COEFFICIENT OF VARIATION
AKA Gaussian Distribution
normal distribution
- Most important distribution
- Describes well the distribution of random variables arise in practice
Normal Distribution
the different measures of Skewness
skewness, kurtosis, extreme values
Horizontal stretching of a frequency distribution to one side or the other, so that the tail of the observations is longer and has more observations than the other tail
Skewness
characterized by a vertical stretching or flattening of the frequency distribution
Kurtosis
values considered to be abnormally far above or below the mean and one of the most perplexing problems for the analysis of data
Extreme Values (outliers):
shows the degree of asymmetry, or departure from symmetry of a distribution
Measures of Skewness
- Distribution tapers more to the right than to the left
- Longer tail to the right
- More concentration of values below the mean
Positively Skewed
- Distribution tapers more to the left than to the right
- Longer tail to the left
- More concentration of values above the mean
Negatively Skewed
