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Descriptive Statistics and Graphical Displays | Circulation

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Descriptive Statistics - Measures of Central Tendency

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The Annals of Statistics

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Dhahran countries please the loginPasswordForgot just '. Dankowitz 28 December In contrast with location statistics, dispersion statistics provide information about the variability of the data about the measures of central tendency. Note that the range is a single value. In the Framingham BMI data, minimum and maximum values are Dispersion about the mean typically is quantified by the variance or the standard deviation.

The variance is defined as the average of squared deviations from the mean. Therefore, it cannot be negative. Its units are the square of the original units of x. To obtain a dispersion statistic with the same units as x , one uses the standard deviation, defined as the square root of the variance. The standard deviation may be regarded as the average deviation from the mean. If all observed values are similar, the standard deviation and variance will be lower than if the values are more spread out.

The interquartile range , abbreviated IQR, is another commonly used dispersion statistic. Whereas variance and standard deviation are affected increased by the presence of extreme observations, the IQR is not; it is robust. The interquartile range for the BMI data is 6.

Materials and methods

Validated outlier observations should be retained in analyses, although secondary analyses to assess sensitivity of major results to outliers may be conducted without them. Two commonly used shape statistics are skewness and kurtosis. In the BMI data Table 2 , the skewness coefficient of 1. If there are no outliers and especially if the distribution is symmetric, the mean and standard deviation are excellent measures of location and dispersion, whereas the median and interquartile range may be more appropriate if outliers or strong skewness is present.

Yet, there is no hard and fast rule. When estimating length of stay or costs associated with a medical condition, skewed data and outliers are common, but means are more appropriate than the medians for planning and administrative purposes. Also, in large samples, outliers are likely to occur, even in gaussian distributions, simply by chance; but if the distribution is reasonably smooth and symmetric, without large gaps between ordered values, the mean and standard deviation are appropriate.