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Chapter 3 Variability

Chapter 3 Variability. Variability. Central tendency tells us about the similarity between scores Variability tells us about the differences between scores -ie. how spread out are the scores in the distribution? -ie. how close or far from the mean are the scores?

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Chapter 3 Variability

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  1. Chapter 3 Variability

  2. Variability • Central tendency tells us about the similarity between scores • Variability tells us about the differences between scores • -ie. how spread out are the scores in the distribution? • -ie. how close or far from the mean are the scores? • There are 3 measures of variability: range, standard deviation & variance Measures of Variability Worksheet (In-Class)

  3. Variability: Range • Symbolized by R • It is the measurement of the width of the entire distribution • To calculate: Subtract the lowest value from the highest value • Least useful measure of variability

  4. Variability: Standard Deviation • Symbolized as SD • The average amount that scores in a distribution deviate from the mean. • The most common descriptive statistic for variability. • Two ways to calculate • -the Deviation Method • -the Computational Method Note: standard deviations are never less than zero because you can’t have less than zero variability.

  5. Variability: Standard Deviation Deviation Method: used as a teaching method to help clearly understand the concept Formula: x=X-M x is the “deviation score” • To calculate: • -find the mean • -subtract the mean of the distribution from each score: (X-M) or x • -square each difference: (X-M)² or x² • -sum the squares • -divide by N • -take the square root

  6. Variability: Standard Deviation Computational Method: is a shortcut that is used most often. -this is what you should use Formula: • To calculate: • -Column 1: sum the raw scores: ΣΧ • -Column 2: square each raw score & then sum the squares: ΣΧ² • -divide the sum of the scores (ΣΧ) by N: M • -divide the sum of the squares (ΣΧ²) by N & subtract the squared mean (M²) • -find the square root

  7. Variability: Variance • Symbolized by V • Measure of how spread out a set of scores are • Average of the squared deviations from the mean • **Also called the “mean square deviation” • To calculate V: calculate the SD but don’t find the square root • **The variance is equal to the SD² • Q:If the variance is just the square of the SD, why use it? • -A: some formulas require using the variance rather than the SD Formula: Measures of Variability Homework due next class

  8. Range & Percentiles • Percentile: the point on a distribution where a given percentage of scores fall below. **EX: 95th percentile means A LOT of scores fall below it **EX: 5th percentile means very FEW scores fall below it -Percentiles are used to show various forms of range -Note: The 50th percentile is right in the middle of the distribution so it is always equal to the median. • Quartiles: divide a distribution into quarters -1st quartile coincides with the 25th percentile -2nd quartile coincides with the 50th percentile -3rd quartile coincides with the 75th percentile

  9. Range & Percentiles • Deciles: divide a distribution into tenths • -1st decile is equivalent to the 10th percentile & so on • -the lowest score would be in the 1st decile & the highest score would be in the 10th decile • Interquartile Range: find the difference between the 1st & 3rd quartiles • -middlemost 50% of the distribution • Interdecile Range: find the difference between the 1st & 9th deciles • -middlemost 80% of the distribution Percentiles Worksheet

  10. Assessing Kurtosis: 1/6th Rule • Use the 1/6th rule to quickly evaluate the kurtosis of any unimodal symmetrical distribution • Mesokurtic distribution: standard deviation is approximately 1/6th of the range -divide the range by 6 to get the approximate standard deviation **EX: R=600 and SD=100 • Leptokurtic distribution: the standard deviation will be LESS than 1/6th of the range **EX: R=600 and SD=50 • Platykurtic distribution: the standard deviation will be MORE than 1/6th of the range **EX: R=600 and SD=200 Pair Share Topic: What does a standard deviation tell you?

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