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### (2) Measure of Spread (Variability / Dispersion)
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A measure of spread, sometimes also called a measure of dispersion or measure of variability is used to describe the variability in a sample or population.
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It is usually used in conjunction with measure of central tendency, such as the mean or median, to provide an overall description of a set of data.
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##### (a) Range
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##### (b) Percentiles/Quartiles
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##### (c) Inter-Quartile Range (IQR)
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##### (g) Kurtosis
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#### (a) Range:
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The range is simply the difference between the maximum and minimum values in a data set.
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##### Range = max - min
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So in a data set of 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 11, 13, 15, 15, 17, 19, 20, the range is the difference between 2 and 20.
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18 = 20 - 2
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While it is useful in seeing how large the difference in observations is in a sample, it says nothing about the spread of the data.
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#### (b) Percentiles/Quartiles
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##### Percentiles divide a data set into 100 equal parts. A percentile is simply a measure that tells us what percent of the total frequency of a data set was at or below that measure.
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##### The Quartiles also divide the data into divisions of 25%, so:
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Quartile 1 (Q1) can be called the 25th percentile
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Quartile 2 (Q2) can be called the 50th percentile
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Quartile 3 (Q3) can be called the 75th percentile
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#### (c) Inter-Quartile Range (IQR)
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The inter-quartile range (IQR) gives more information about how the observation values of a data set are dispersed. It shows the range of the middle 50% of observations.
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#### (d) Variance
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##### Deviation: The difference between each xi and the mean is called deviation about the mean
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##### Variance: is based on deviations and entails computing square of deviations
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##### Population Variance: Average of Standard Deviations
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##### Sample Variance: sum of square deviations divided by n-1
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#### (e) Standard Deviation
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The standard deviation indicates the average distance between an observation value, and the mean of a data set. In this way, it shows how well the mean represents the values in a data set. Like the mean, it is appropriate to use when the data set is not skewed or containing outliers.
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#### (f) Skewness
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In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or undefined.
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#### (g) Kurtosis
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In probability theory and statistics, kurtosis is a measure of the "tailedness" of the probability distribution of a real-valued random variable.
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