Statistics: Measures of Variability

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Questions and Answers

What does variability primarily measure?

  • The spread between scores (correct)
  • The average score in a data set
  • The deviation from the median
  • The total number of scores

Which measure ignores individual data points while providing a summary?

  • Standard deviation
  • Range (correct)
  • Mean
  • Variance

What is the formula for variance?

  • Variance = SS/N
  • Variance = SS/N-1 (correct)
  • Variance = (Highest - Lowest)/Number of values
  • Variance = Sum of deviations squared

How is deviation defined in relation to the mean?

<p>Deviation = (X - mean) (A)</p> Signup and view all the answers

What does variance specifically measure?

<p>The average of variability represented by squared deviations (A)</p> Signup and view all the answers

What is the result of calculating the sum of squared deviations?

<p>A component needed to calculate variance (C)</p> Signup and view all the answers

Which of the following is NOT a way to measure variability?

<p>Mean (B)</p> Signup and view all the answers

Which measure is considered the reverse of variance?

<p>Standard deviation (B)</p> Signup and view all the answers

Calculate the deviation.

<p>4.83</p> Signup and view all the answers

Calculate the variance.

<p>0.66</p> Signup and view all the answers

Flashcards

Variability

A measure of the spread of scores in a dataset.

Range

The difference between the highest and lowest scores in a dataset.

Deviation

The distance of each score from the mean.

Variance

The squared average of deviations from the mean.

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Standard Deviation

The square root of variance.

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Sum of Squares (SS)

The sum of squared deviations from the mean.

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Variance Formula

The formula to calculate variance is SS/(N-1), where SS is the sum of squares and N is the number of scores.

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Sum of Deviations

The sum of deviations is always zero.

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Study Notes

Variability Summary

  • Variability measures the spread of scores.

Ways of Measuring Variability

Range

  • Ignores most data points, only considering the highest and lowest values.
  • Formula: Range = Highest Score - Lowest Score

Deviation

  • Measures the distance of a score from the mean.
  • Deviation is the opposite of variance.
  • Formula: Deviation = (X - )
  • Variability = Σ(score - mean)²
  • Uses the mean value for calculation.

Variance

  • Averages the squared deviations.
  • Provides a more comprehensive measure of variability.
  • Formula: Variance = S² = SS/(N-1)
  • SS is the Sum of Squares.
  • N is the number of observations.
  • Standard deviation is the square root of variance.

Sample Variance Calculation

  • For a sample: s² = SS/(N-1)
  • ΣΧ² - (ΣΧ)²/N
  • Dividing by (N-1) instead of N gives a better estimate of the population variance.

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