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• Measures of dispersion indicate the extent to which individual items in a series are scattered about an average.
• Measures of dispersion are used to determine the extent of scatter and to measure the reliability of the average value.
• There are two general classifications of measures of dispersion: measures of absolute dispersion and measures of relative dispersion.
• Range is the distance covered by the scores in a distribution, from the smallest score to the largest score.
• The range is approximated by getting the difference between the upper class limit of the highest class interval and the lower class limit of the lowest class interval.
• Range uses only the extreme values and fails to communicate any information about the clustering or lack of clustering of the values between the extremes.
• An outlier can greatly alter the value of the range.
• Range cannot be approximated from open-ended frequency distributions and is unreliable when computed from a frequency distribution table with gaps or zero frequencies.
• The initial HDL cholesterol values of participants are 31, 41, 44, 46, 47, 47, 48, 48, 49, 52, 53, 54, 57, 58, 58, 60, 60, 62, 63, 64, 67, 69, 70, 77, 81, and 90 mg/dL.
• The highest value is 90 mg/dL and the lowest value is 31 mg/dL.
• The range is calculated as 90 - 31 = 59 mg/dL.
• Variance is the mean of the squared deviations from the mean.
• Variance is calculated as (x1 - x̄)² / (N - 1) or (x1 - μ)² / N.
• Variance shows how widely the individual figures in a set of data distribute themselves about the mean.
• Mean is calculated.
• Deviations from the mean are calculated.
• The deviations are squared.
• The squared deviations are added together.
• The sum is divided by the number of items for which the variance is being calculated.
• A variance of zero value means all the data are identical.
• More the variance, more are the values spread out about the mean, hence from each other.
• Less the variance, less are the values spread out about the mean, hence from each other.
• Variance can't be negative.
• For an observed set of data, when the denominator of the equation for variance is expressed as the number of observations minus 1 (i.e. N-1), the variance of a random sample is an unbiased estimator of the variance of the population from which it was taken.
• It fails to communicate any information about the clustering or the. (incomplete sentence)
• Standard deviation 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 is the most commonly used and important measure of variability.
• Standard deviation is affected by the value of every observation and may be distorted by few extreme values.
• Standard deviation 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 standard deviation of the new set remains the same.
• The standard deviation of a new data set is the same as the standard deviation of the original data set.
• If a data set is transformed by multiplying/dividing each observation by a constant "c", the standard deviation of the new data set is equal to the standard deviation of the original data set multiplied/divided by "c".
• Population standard deviation is used when making a statement about the population from which the sample is drawn.
• Sample standard deviation is used when you have a sample of a larger population and you do not wish to generalize your findings to the population.
• Sample standard deviation (s) is a measure of the scatter of data points around the mean.
• Coefficient of Variation (CV) is the ratio of the standard deviation to the mean, usually expressed as a percentage.
• CV is used to compare the dispersion of data between different distributions.
• CV can be calculated for both population and sample data.
• CV is a statistical measure of the dispersion of data points around the mean.
• CV is used to compare data dispersion between distinct series of data.