Measures of Central Tendency PDF

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Measures of Central Tendency. Statistics notes Lecture 2 part 1....

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Measures of Central Tendency 

Descriptive Statistics: Major Points o Measures of Central Tendency  Summary measures (single number) that describes multiple observations (data).  What is the usual (central/average) observation (thing/person)?  Mean, median, mode. o Variability: summary measures assessing the degree to which observations (data) close to the central point – are they similar or dissimilar (dispersion).  Are things/persons clustered together or far apart? Range, standard deviation, graphical histogram? o Covariability: the degree to which variability on one characteristic/aspect of a thing/person/observation give us information about another characteristic/aspect.  Mean differences, correlation, graphical scatter plot.

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Central Tendency o Mean: or arithmetic mean is the sum of the values divided by the number of observations. o Median: middle-most score; the 50th percentile, or the point at which 50% (half) of the scores lie below and above. o Mode: observation that occurs most frequently.  Can be employed with nominal/categorical or quantitative data, whereas median and mean apply only to quantitative data.

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Descriptive Statistics o N refers to the number of scores. o M refers to the arithmetic mean. o Σ = sum; add up.  Capital Greek letter Sigma – the symbol for the summation operation.

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Mean (μ) o X – 1, 3, 4, 5, 6, 8, 8. o “N” will refer to the number of scores. o N=7 o “M” = arithmetic mean. o Σ = sum; add up.

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Median (Med) o X – 1, 3, 4, 5, 6, 8, 8. o First place scores in order. o Median location (N+1)/2.  Example: (7+1)/2=4 (4th score in order) o 4th score is 5 o Divides distribution in half. o Aka. The 50th percentile; 50% of the scores in the distribution are at or below the median.

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Mode (Mo) o Mode is the score which appears most frequently: 8.

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Central Tendency o Properties of Mean (vs. median and mode)

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 Sum of the squared deviations is a minimum. That is, you can’t take any other score and subtract is from the set of scores that will result in a lower score.  Mean is highly influenced by outliers (median and mode are not).  Mean is the least influenced by “sampling” variability (mode the most). 

What is a Normal Curve o 1 possible distribution of data o Normally distributed  Raw data falls around 1 central value.  Mean  Median  Mode  Outliers at both ends  No skew.

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