Is it true to say that the mean, mode and median of grouped data will always be different? Justify your answer.

The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement? Give reason.

In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula,

Where, is the assumed mean, must be one of the mid - point of the classes. Is the last statement correct? Justify your answer.

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

In a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is 1/4. Is this correct? Justify your answer.