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Step-by-Step Explanation
1. Understanding Statement (a):
Statement (a) says, “Mode can be computed from histogram.” In a histogram, each bar represents the frequency of a range or class of values. The tallest bar corresponds to the class with the greatest frequency, indicating the mode. Hence, it is correct that one can visually determine the modal class (and often approximate the mode) from the highest bar in the histogram.
2. Understanding Statement (b):
Statement (b) says, “Median is not independent of change of scale.” The median is the middle value when data are arranged in ascending or descending order. If we multiply (or divide) every data point by a constant (a process known as a change of scale), each position in the ordered list is similarly affected, and thus the median's numerical value will also be multiplied (or divided) by that constant. Therefore, the median depends on the change of scale, making statement (b) correct.
3. Understanding Statement (c):
Statement (c) says, “Variance is independent of change of origin and scale.” The variance of a dataset is indeed independent of change of origin (adding or subtracting the same constant from all data points). However, it is not independent of change of scale. If every value in the dataset is multiplied by a constant $k$, the variance gets multiplied by $k^2$. Hence, while it is independent of change of origin, it is not independent of the change of scale, making statement (c) incorrect as stated.
4. Conclusion:
From the above points, we see that statements (a) and (b) are correct, while statement (c) is incorrect in claiming independence from scale. Therefore, the correct option is “only (a) and (b).”
