2 Central Tendency

Eamonn Mallon
11/06/2019

Descriptive statistics

height

  • Measurements often cluster around intermediate values (central tendency)
  • Variability of a sample is perhaps the most important quantity in data analysis

Central tendency

How should we quantify the central tendency

height

  • We will look at three different ways to look at the “average”, commonly used in biology
  • Lets start with the mode, the data values that occur the most frequently
  • The easiest way of calculating that is just looking at the data

Lets just look at the data

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The mode

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The arithmetic mean

Figure showing UK income distribution

  • \( \bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_{i} \)
  • sum of a collection of numbers divided by the count of numbers in the collection
  • not a robust statistic, meaning that it is greatly influenced by outliers
  • http://tiny.cc/es6l9y

The median

Figure showing UK income distribution

  • The middle value
  • 3,5,6,8,10 (median = 6)
  • 3,5,6,8,10,10 (median = 7), work out the average value of the two numbers either side of the middle

Descriptive statistics

height

  • Measurements often cluster around intermediate values (central tendency)
  • Variability of a sample is perhaps the most important quantity in data analysis