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

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.

Is it true to say that the mean, mode and median of grouped data will 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.

A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3) (see figure). Are the outcomes 1, 2, and 3 equally likely to occur? Give reasons.