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(i). Mean, median and mode are measures of central tendency.

A central tendency (or measure of central tendency) is a central or typical value for a probability distribution.

Mean gives us the average of given set of values or variables, which is the central value in a set of values.

Median is a value separating higher half from the lower half of the data, which gives us the central measure.

Mode is the value in the data occurring most often, gives an indication of the central value in the data.

(ii). If mean of is mean of is .

Given that, mean of x₁, x₂, x₃, …, x_n is .

⇒

⇒

⇒ x₁ + x₂ + x₃ + …+ x_n = n …(1)

Then, mean of ax₁, ax₂, ax₃, …, ax_n is given by

⇒

⇒

⇒ Mean = a

(iii). At the time of finding arithmetic mean, the lengths of all classes are not necessarily equal.

It is not necessary for class intervals to be equal but it would be better if class interval size is smaller. But at the time of finding arithmetic mean, equal or unequal class interval can yield result.