Q.Some measures of dispersion depend upon the spread of values whereas some are estimated on the basis of the variation of values from a central value. Do you agree?

The four numerical measures fall neatly into two families depending on what they actually measure.

Yes, this statement is correct. The four numerical measures of dispersion fall into two groups:

1. Measures based on the spread of values.

   • Range $= L - S$ measures the total spread between the largest and smallest values.
   • Quartile deviation $= \dfrac{Q_3 - Q_1}{2}$ measures the spread of the middle 50% of the values. These describe dispersion by the interval within which (all or most of) the values lie, without reference to an average.

2. Measures based on deviation from a central value.

   • Mean deviation $= \dfrac{\sum |d|}{n}$ is the average of the absolute deviations of the values from their mean or median.
   • Standard deviation $\sigma = \sqrt{\dfrac{\sum d^2}{n}}$ is the square root of the mean of the squared deviations from the mean. These measure how far, on average, the values lie from their average.

So the classification in the statement is valid: range and quartile deviation depend on the spread of values, while mean deviation and standard deviation are estimated from the variation of values around a central value.