Will the median class and modal class of grouped data always be different? Justify your answer.

Is it trun to say that the mean, mode and median of group data will always be differnet? Justify your answer.

The median and modal classes of the following data :

Is inclusion of a subset in another, in the context of a universal set, an equivalence relation in the class of subsets of the sets? Justify your answer.

The modal class of the data given below is ________.

In Calculating the mean of grouped data, grouped in classes of equal width, we may use the formula bar(x)=a+(sumf_(i)d_(i))/(sumf_(i)) Where, a is the assumed mean, a must be one of the mid point of the classes. Is the last statement correct? Justify your answer.