Summary Measures of Data

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Summary Measures:

Measures of central tendency:
Mean (arithmetic average), median (value associated with 50th percentile) and mode (value that occurs most frequently) are measures of central tendency

Guidelines for use:
• Mode – a rough estimate of mean if data is normally distributed
• Median – if data is on an ordinal scale; if the middle value of a group is needed; if the most typical value is needed; if the distribution curve is skewed by outliers
• Mean – if data is normally distributed; if all information about the data set is needed; if further calculations are to be made (eg standard deviations).

Measures of variability:
Central tendency measures do not give an indication of the spread of values about the central measure, so measures of variability or dispersion are used:
Range – difference between highest and lowest value in the dataset – like the mode, it is only real an estimate of variability and is unstable as it is influenced by outliers or extreme values.
Inter-quartile range (IQR) – difference between upper and lower quartiles (range is influenced by outliers, but the inter-quartile range is not) – considers only middle 50% of data set. Like the median, it presents a typical picture, but does not consider all the information in the data set.
Variance – variance is calculated by taking the squares of the differences of each observation from the mean and adding them – this is then divided by the number of observations minus one (if it’s a sample of a population*) or by the number of observations (if it’s a population dataset*). The sum of these squared deviations is called the sum of squares (SS). The mean of these squared deviations is called the mean square (MS). Thus the variance is the average of the squared deviations from the mean.
Standard deviation – square root of the variance
Coefficient of variation – a ratio – standard deviation divided by the mean x 100. Expresses standard deviations as a proportion of the mean  measure of relative variation.

* the variability of a sample is never as large as the variability of a population, so a correction factor is applied to the formula for variance. This correction is based on degrees of freedom.

Sources of variability:
• experimental or imprecision error
• biological variability
• mistakes

Skewness:
A measure of the bilateral symmetry of the data

Kurtosis:
Measure of the relative ‘peakedness’ of the data.

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Page last updated: Dec 6, 2022 @ 4:52 am

 
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