Final answer:
The measure of variability in question is the variance, which is the mean of the squared deviations from the mean minus 1 and is expressed in squared units. The correct answer is C.
Step-by-step explanation:
The measure of variability that involves squaring the difference scores but does not involve taking their square root is the variance. For a set of data, a deviation can be represented as x - × where x is a value of the data and × is the sample mean. The sample variance is calculated by taking the sum of the squares of these deviations and then dividing by the difference of the sample size and 1 (n - 1). The variance is a measure in square units because the individual differences between the data points and the mean are squared, thereby squaring the unit of measure.
In contrast, the standard deviation is a measure that is equal to the square root of the variance and provides the spread of the data in the same units as the data itself. The range and mean absolute deviation, other measures of spread, involve the actual differences without squaring or taking the square root of those differences. Consequently, the correct answer to the student's question is variance, which reflects the squared deviations from the mean.