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Lecture 4-5 Central Tedencies

# Lecture 4-5 Central Tedencies - Operationalizing Central...

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Operationalizing Central Tendency What constitutes an intelligible and informative measure of central tendency in a distribution? 1) The score or category at which the distribution peaks 2) The score or rank that divides a distribution in half 3) The score that balances the distribution; center of gravity 1

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Mode Where the distribution peaks; the most typical measurement class Qualitative/ranked data - the category with the highest frequency count Discrete variables - the most frequently observed score Continuous variables - the midpoint of the most frequently observed measurement class 2
Mode: Pros and Cons Pros: Appropriate for qualitative data Easy to determine Captures the shape of the distribution (bimodal distributions) Not influenced by extreme scores 3

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Mode: Pros and Cons Cons: Ignores most of the information in a data set Unstable for samples from populations with flat distributions (kurtosis) May be undefined for small data sets Problematic with continuous data Not mathematically tractable (i.e., a terminal statistic - not useful in higher level statistics) 4
Median The score that divides the distribution into two groups with equal frequencies 1) Order observations from least to greatest 2a) If n = ƒ is odd, count in ( n +1)/2 steps from either end. That is the median. 2b) If n = ƒ is even, find the scores corresponding to positions ( n /2) and ( n / 2)+1 , add them together, and divide by 2.

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Lecture 4-5 Central Tedencies - Operationalizing Central...

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