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MEASURES OF CENTRAL TENDENCY CHAP. 4

MEASURES OF CENTRAL TENDENCY CHAP. 4 . James A. Van Slyke . CENTRAL TENDENCY AND VARIABILITY . Central Tendency - Calculating the average score for any group of scores Mainly used as a means of comparison Variability – how the scores vary in comparison to each other

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MEASURES OF CENTRAL TENDENCY CHAP. 4

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  1. MEASURES OF CENTRAL TENDENCY CHAP. 4 James A. Van Slyke

  2. CENTRAL TENDENCY AND VARIABILITY • Central Tendency - Calculating the average score for any group of scores • Mainly used as a means of comparison • Variability – how the scores vary in comparison to each other • Grouped together, spread out, etc. • How much do the scored vary in regards to the central tendency

  3. MEASURES OF CENTRAL TENDENCY • Arithmetic Mean • The Average score • Sum of the scores divided by the number of scores • Sample mean • Population mean • Computations are the same for a sample or population

  4. PROPERTIES OF THE MEAN • Sensitive to the exact values of each score • Sum of the deviations from the mean is always equal to zero • The mean is affected by extreme scores or outlying scores • Least affected by sampling variation

  5. MEDIAN • Score below which 50% of the scores fall • Same as the Percentile point P50 • For raw ungrouped scores the median is: • Center score if the scores are an odd number • Average of the two center scores center if the scores are an even number

  6. MEDIAN • Properties • Less sensitive to extreme or outlying scores than the mean • Effected more by sampling variability than the mean

  7. MODE • Simply put, the most frequently given score in a distribution – thus no calculation is necessary • Unimodal – distribution with one mode • Bimodal – distribution with two modes

  8. MEASURING CENTRAL TENDENCY • If a particular distribution is unimodal and symmetrical • Mean, median, and mode are equal • bell-shaped curve; normal curve • Skewed distribution • Mean and median are not equal • Positive – mean larger than the median • Negative – mean is smaller than the median

  9. STANDARD DEVIATION • Deviation score – shows the distance between the mean and a particular score • Sample deviation score • Population deviation score

  10. STANDARD DEVIATION • Because the sum of the mean always equals zero, each standard deviation score must be squared • This is the sum of squares or the sum of standard deviations

  11. STANDARD DEVATION • Standard deviation score of a population • Deviation Method • Better for whole numbers • Not good for decimals

  12. STANDARD DEVIATION • Deviation Method for sample scores • Same as for population scores but N is decreased by one • Runs into same computation problems

  13. STANDARD DEVIATION • Raw Scores Method • First calculate the Sum of Squares • Then calculate the standard deviation

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