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Central Tendency Mean: what most call “average”

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Presentation on theme: "Central Tendency Mean: what most call “average”"— Presentation transcript:

1 Central Tendency Mean: what most call “average”
Describes a distribution through numerical account of the centre of a distribution. Mean: what most call “average” > res<-c(21,18,12,31,23,31,44,7) > mean(res) [1] SPSS: Analyze Menu, Descriptive Statisitcs

2 Central Tendency Describes a distribution through numerical account of the centre of a distribution. Median: the variate with the same number of variates both greater and less than it; the centre variate in an ordered array > res<-c(21,18,12,31,23,31,44,7) > median(res) [1] 22 SPSS: Analyze Menu, Descriptive Statisitcs

3 Central Tendency Describes a distribution through numerical account of the centre of a distribution. Mode: the variable class with the greatest abundance or highest frequency > res<-c(21,18,12,31,23,31,44,7) > library(modeest) > mfv(res) [1] 31

4 Which Measure? What best characterises the centre of the distribution? What measures are most affected by outliers? Y=23.4, median=22, mode=31

5 Dispersion Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency.

6 Dispersion Range: difference between largest and smallest variates
Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency. Range: difference between largest and smallest variates > res<-c(21,18,12,31,23,31,44,7) > max(res)-min(res) [1] 37

7 Dispersion Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency. Interquartile range: characterizes the middle 50% of a distribution by subtracting the 25th percentile from the 75th percentile. 1st quartile 2nd quartile 3rd quartile Yi Sorted 7 18 12 21 23 31 44 > res<-c(21,18,12,31,23,31,44,7) > IQR(res)

8 Dispersion Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency. Variance & Standard Deviation: provide a combined measure of every variates’ deviation from the mean (compare to spread between only two variates using range or IQR)

9 Dispersion Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency. Variance: think of “average” squared deviation from the mean Variance is good for some kinds of distribution comparisons, but s2 not in original units > res<-c(21,18,12,31,23,31,44,7) > var(res)

10 Dispersion Standard Deviation: average deviation from the mean
Measures of dispersion tell us about a distribution’s shape or the spread of variates around the central tendency. Standard Deviation: average deviation from the mean > res<-c(21,18,12,31,23,31,44,7) > sd(res) [1]

11 Comparing Dispersions
Comparing s of distributions of different “sized” things not useful The size of s is determined by value of variates. Larger Ys (e.g., length of primate humeri) create larger s than smaller Xs (e.g., length of rat femurs) Primate humeri & rat femurs

12 Comparing Dispersions
Coefficient of variation “standardizes” standard deviation by the mean Comparisons must use same units From: Pattern and Process in Cultural Evolution (2009), edited by S. Shennan, pp University of California Press.


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