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FM Interquartile Range

1.6 Describing Numerical Distributions

Shape

  • The shape of a numerical distribution relies on two factors: symmetry and outliers.
  • If you can draw a vertical line through some point in the distribution whereby the distribution to the left of the line looks similar to a mirror image of the distribution to the right of it, it is an approximately symmetrical distribution. If this is not the case, the distribution is asymmetric.

Note: in some cases, you may find situations where the distribution has perfect symmetry. In these situations, you can drop the “approximately” term and refer to it simply as symmetrical.

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1.5 Basic Statistical Concepts

Mean

  • The mean of a numerical distribution is found by summing up the values of all individual data points, then dividing by the number of data points.
  • It is represented by either a capital letter with a bar drawn above it, or the Greek symbol mu (µ):

\bar{X}=\frac{\sum_{i=1}^{N} x_{i}}{N}

Where N is the total number of data points, and represents the i’th datapoint.

Note: the symbol \Sigma is short for “sum of”, so \sum_{i=1}^{N} x_{i} represents the sum of all individual data points (from datapoint 1, to datapoint N)

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