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Variability

Variability. Chapter 4 (part 2). Calculating Standard Deviation. First Step: Calculate the deviation from the mean Create a column for X- μ and calculate the value for each score. Second Step: Calculate the mean of the deviation scores M =∑(X- μ )/N Third Step:

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Variability

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  1. Variability Chapter 4 (part 2)

  2. Calculating Standard Deviation First Step: Calculate the deviation from the mean Create a column for X-μ and calculate the value for each score. Second Step: Calculate the mean of the deviation scores M=∑(X-μ)/N Third Step: Calculate the variance Variance=∑(X-μ)2/N Fourth Step: Calculate the Standard Deviation Std. Deviation = √variance

  3. Population Parameter Sample size=N Mean=μ Definitional Sum of Squares = SS=∑(X-μ)2 Comp. Sum of Squares = SS= ∑X2 – (∑X)2 N Variance = σ2 = SS N Std. Deviation = σ = √variance = √ σ2 Sample Statistic Sample size=n Mean=M Definitional Sum of Squares = SS=∑(X-M)2 Comp. Sum of Squares = SS=∑X2 – (∑X)2 n Variance = s2 = SS (n-1) Std. Deviation = s = √variance = √ s2 N (population) & n (sample)

  4. SS (Def.), Variance & Std. Dev. for Populations First Step: Identify the N Second Step: Compute Mean Third Step: Create a column for X-μ and calculate the value for each score. Fourth Step: Create a column for (X-μ)2 and square each value in previous column. Fifth Step: Sum all values in (X-μ)2 to get SS. Then compute variance and Standard deviation using the SS value. Raw Scores: 4, 7, 3, 1, 5

  5. SS (Def.), Variance & Std. Dev. for Samples First Step: Identify the n Second Step: Compute Mean Third Step: Create a column for X-M and calculate the value for each score. Fourth Step: Create a column for (X-M)2 and square each value in previous column. Fifth Step: Sum all values in (X-M)2 to get SS. Then compute variance and Standard deviation for samples using the SS value in the formula. Raw Scores: 4, 7, 3, 1, 5

  6. The graphic representation of a population with a mean of  = 40 and a standard deviation of  = 4.

  7. The set of all the possible samples for n = 2 selected from the population described in Example 4.7. The mean is computed for each sample, and the variance is computed two different ways: (1) dividing by n, which is incorrect and produces a biased statistic; and (2) dividing by n– 1, which is correct and produces an unbiased statistic.

  8. A sample of n = 20 scores with a mean of M = 36 and a standard deviation of s = 4.

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