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Q: You know the minimum the maximum and the 25th 50th and 75th percentiles of a distribution. what measures of central tendency or variability can you determine?

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Why are measures of variability essential to inferential statistics?

The usual measures of variability cannot.

The answer lies in the question! The first lot measure where the centre of a distribution or observation lies while the second lot are a measure of the distance of individual observations from the centre.

The best measure of variability depends on the specific characteristics of the data. Common measures include the range, standard deviation, and variance. The choice of measure should be made based on the distribution of the data and the research question being addressed.

Median, mode, quartiles, quintiles and so on, except when you get to very large number of percentiles.

The range, inter-quartile range (IQR), mean absolute deviation [from the mean], variance and standard deviation are some of the many measures of variability.

It measures the error or variability in predicting Y.

Standard error, standard deviation, variance, range, inter-quartile range as well as measures based on other percentiles.

The distribution is skewed to the right.

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