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Variability - Coggle Diagram
Variability
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Range
Range: The distance covered between scores in a dsitribution from the smallest score to the largest score.
It cab be calculated by the formula:
Range= X max - X min
When scores are measurements for continuous variables, an alternative formula is used to find range:
Range = Upper real limit for Xmax - Lower real limit for Xmin
Variability: A qualitative measure of the differences between scores in a distribution and describes the degree to which these scores are spread out or clustered together. Simply put, variability allows us to observe a distribution.
Variability serves two purposes:
- Describes the distribution of scores or data. variability describes how much distance is between one score and another.
2.Desribes how well one score can represent the entire distribution.
The Problem with Sample Variability: A sample statistic is said to be biased if it always overestimates or underestimates the population parameters. Fortunately, this can be corrected.
Finding the variance and standard variation for a sample is the same for a sample as it is for a population.The notation is the only thing that changes.
Definitional formula = ∑(X-M)^2
This formula tells us to find the deviance from mean to score (X-M).Then, square each deviation or (X-M)^2
Finally, find the sum of the squared deviations
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Degrees of freedom: Determine the number of scores that are independent and free to vary.
The formula for df = n - 1
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Transformation of scale:
- Adding a constant to the score does not change the standard deviation.
- Multiplying each score by a constant causes the standard deviation to be multiplied by the same constant.
Because we are adding or multiplying the constant to every score the effects will be the same.