Measurement

Keep three things apart: the variable is height, the observational unit is student 12, and the measurement is the number 168 centimeters that ties them together. Measurements carry units and a level of precision, so the same underlying quantity can be recorded on different scales. For example, a height of 168 centimeters becomes $168 / 2.54 = 66.14$ inches, which divides the mean and the standard deviation by 2.54 but leaves the shape of the distribution and any correlation unchanged. Recording to the nearest centimeter also builds in rounding, one reason repeated measurements of the same object are not identical.