Notes > Foundations of Computing > Measures of Spread / Dispersion
The Range is the difference between the largest and smallest value. The range does not describe in any way how the values are distributed within the range but it simply gives the difference between the minimum and maximum values and this of course includes any extreme outlying values that may be present.
The Quartiles divide the set of data into 4 quarters where the lower quartile (Q1) has 25% of all the data below it and the rest is above it. The middle quartile (Q2) is the same as the median. The upper quartile (Q3) has 25% of the data above it. The positions of the quartiles are calculated by adding 1 to the total number of values (n) then multiplying the result by 1/4, 1/2, and 3/4 to find Q1, Q2, and Q3 respectively.
The inter-quartile range is the difference between the upper and lower quartile (Q3-Q1). The "quartile deviation" or "semi-inter-quartile range" is half the inter-quartile range.
Standard Deviation is the most common measure and is useful for more in-depth data analysis. It involves finding the square root of the average squared distances from the mean. The "variance" is simply the square of the standard deviation. With two sets of data that have the same mean but are spread differently, the standard deviation will be different. A tight set of data with a small range will have a smaller standard deviation.
Skewness is the measure of how symmetrical a distribution of values is. If the set of data has a "tail" toward the higher values on the scale i.e. it has the majority of its values bunched toward the lower end of the scale, then this set of data is said to be positively skewed. The opposite of this is negative skewness.
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