JEE Main 2004 — Statistics Question with Solution

The statements are analyzed as follows :

(a) Mode can be computed from histogram : This is correct. The mode is the value that appears most frequently in a data set. A histogram provides a graphical representation of the frequency of each data value. The data value corresponding to the highest bar in a histogram is the mode.

(b) Median is not independent of change of scale : This is correct. The median is the middle value in a data set when the values are arranged in ascending or descending order. When you change the scale (e.g., by multiplying all data points by a constant), the median changes as well.

(c) Variance is independent of change of origin and scale : This is not correct. Variance, which measures the dispersion of a set of data points, is affected by changes in scale (it is not independent of scale). If you multiply all the values in a dataset by a constant, the variance gets multiplied by the square of that constant. However, it is true that variance is independent of the change of origin (it remains the same if you add or subtract a constant from all data points in the set).

Therefore, the correct answer is Option C : only (a) and (b) are correct.