If every observation in a data set is multiplied by 10, the...

If every observation in a data set is multiplied by 10, the only one of the following that is not multiplied by
10 is
(a) the mean. (d) the standard deviation.
(b) the median. (e) the variance.
(c) the IQR.

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Key Concepts

Linear Transformation

A linear transformation involves multiplying each data observation by a constant. This transformation linearly affects many statistical measures, meaning that measures of central tendency (like the mean and median) are multiplied by the constant factor. However, some measures of variability are affected non-linearly by such a transformation.

Effect on Measures of Central Tendency

When every observation in a dataset is multiplied by a constant, measures of central tendency, such as the mean and median, are also multiplied by that constant. This preserves the relative order and positions of the data values without distorting their shape.

Effect on Measures of Dispersion

Measures of dispersion, which describe the spread of data, react differently to scaling: the standard deviation is multiplied by the constant, whereas the variance, being the square of the standard deviation, is multiplied by the square of that constant. This is a critical distinction when analyzing how transformations affect spread in the data.

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