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Variability: quantitative measure for differences between scores in a…
Variability: quantitative measure for differences between scores in a distribution
Can be used to measure consistency, predictability, or diversity.
Range: distance covered by scores in the distribution from smallest to largest score.
For a continuous variable, the range can be defined as the difference between the upper real limit for the largest score and the lower real limit for the smallest score.
Standard Deviation: provides a measure of the standard, or average, distance from the mean and describes whether those scores are clustered closely together or widely scattered.
Variance equals the mean of the squared standard deviations or the average squared distance from the mean.
Deviation score formula:
Step 2: Compute mean of deviation scores.
Step 3: Square each deviation score and compute average of these scores which will result in the variance.
Step 4: Take square root of variance to obtain standard deviation.
Sum of Squared Deviations found using two formulas: Definitional and Computational
Sequence of calculations for definitional formula:
Definitional:
Useful when deviations are whole numbers
Computational:
Useful when deviations are fractions or decimals.
Population and Sample Variance
Population variance is obtained by dividing the Sum of Squares by N.
Population standard deviation is equal to the square root of the population variance.
Statistics are biased if they consistently over or underestimate the corresponding population parameter.
Sample variance is equal to the mean squared distance from the mean. Divide sum of squares by n.
Sample standard deviation is the square root of the variance
Sample Bias:
Unbiased: average value of the statistic is equal to the population parameter.
Biased: average value of the statistic either over or underestimates the corresponding population parameter.
Frequency Distribution Graph
