lecture 2: part b

• The measures of dispersion (variability) are descriptive statistics that

  describe how similar a set of scores are to each other.
• Range (R) is the difference between the largest and the smallest

  values in a set of data.
• Interquartile range (IQR) is obtained by subtracting the first quartile from the third quartile
• Standard deviation – is the square root of the sum of the squared differences around the arithmetic mean divided by the number of observations.
• Variance – is squared standard deviation
• The variance and standard deviation measure the “average” scatter around the mean; ( how larger observations fluctuate above it and how smaller observations distribute below it)
• Variance possesses certain mathematical properties but its computation results in squared units.
• Coefficient of Variation (CVSx) - is a relative dispersion measure obtained by dividing the standard deviation of the scores by the arithmetic mean.
• A mathematical theorem called Chebyshev’s theorem establishes the

  following rules: 1. At least three-quarters of the observations in a set will lie within 2 standard deviations of the mean.

  2. At least eight-ninths of the observations in a set will lie within 3 standard deviations of the mean
• Positive skewness arises when the mean is increased by

  some unusually high values
• Negative skewness arises when the mean is reduced by some

  extremely low values.
• Pearson’s mode coefficients of skewness: To describe the shape, we need only to compare mean and mode
• Coefficient of skewness is normalized in the interval <-1; 1>
• if the mean exceeds the mode (As>0) - the data may generally be

  described as positively asymmetrical or right-skewed
• if the mean is exceeded by the mode (As<) the data are called

  negatively asymmetrical or left-skewed