How to measure the distribution of variables?

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Usually, we look at two characteristics of the distribution of a continuous variable: central tendency and dispersion.

The most basic measure of variation is the range, which is the distance from the smallest to the largest value in a distribution. However, the range uses only two values in the data set, and these values may be unusually large or small. Compared to the range, the interquartile range (IQR) is affected less by the extreme values. It is the range of the middle 50% scores in a distribution: IQR= 75th percentile – 25th percentile.

The standard deviation is the average amount by which scores differ from the mean. The standard deviation is the square root of the variance, and it is a useful measure of variability when the distribution is normal or approximately normal. A small standard deviation coefficient indicates a small degree of variability (that is, scores are close together); larger standard deviation coefficients indicate large variability (that is, scores are far apart).