What term describes the average of the squared deviations from the mean, whose unit is on a larger scale than that of the original data?

The term that describes the average of the squared deviations from the mean is variance. Variance measures how much the values in a dataset differ from the mean. By squaring the deviations, variance emphasizes larger differences and ensures that all values contribute positively to the measure, as it removes the impact of negative deviations.

The unit of variance is the square of the original data's unit, which indeed places it on a larger scale than the original data. For example, if the data is in meters, the variance will be in square meters. This characteristic of variance is crucial when performing statistical analyses, as it serves as a foundational concept in understanding data spread and variability.

Kurtosis measures the "tailedness" or the shape of the distribution of data points, while standard deviation, on the other hand, is the square root of variance and returns the measure back to the original data's unit, making it smaller in scale than variance. Quartile deviation focuses on the data's distribution relative to quartiles and does not capture the overall variability in the same way that variance does. Thus, variance stands out as the term that accurately describes the average of the squared deviations from the mean.