Consider the following statements :
(i) Mode can be computed from histogram.
(ii) Median is not independent of change of scale.
(iii) Variance is independence of change of origin and scale.
Which of these is/are correct :

Options

A. only (i)
B. only (ii)
C. only (i) and (ii)
D. (i), (ii) and (iii)

Answer

To solve the question, we will analyze each of the three statements one by one to determine their validity.

### Step 1: Analyze the first statement
**Statement (i): Mode can be computed from histogram.**

- **Explanation**: The mode of a dataset is the value that appears most frequently. A histogram is a graphical representation of the distribution of numerical data, and it shows the frequency of data points in different intervals (bins). By examining the histogram, we can identify the bin with the highest frequency, which corresponds to the mode of the dataset.

- **Conclusion**: This statement is **True**.

### Step 2: Analyze the second statement
**Statement (ii): Median is not independent of change of scale.**

- **Explanation**: The median is the middle value of a dataset when it is ordered. If we change the scale of the data (for example, by multiplying all values by a constant), the position of the median can also change. Therefore, the median is affected by changes in scale.

- **Conclusion**: This statement is **True**.

### Step 3: Analyze the third statement
**Statement (iii): Variance is independent of change of origin and scale.**

- **Explanation**: Variance measures the spread of a set of values. It is affected by changes in scale (e.g., if all values are multiplied by a constant, the variance will be multiplied by the square of that constant). However, variance is independent of changes in origin (adding a constant to all values does not affect the variance). Therefore, this statement is misleading as it implies that variance is independent of scale, which is not true.

- **Conclusion**: This statement is **False**.

### Final Conclusion
- The first statement is **True**.
- The second statement is **True**.
- The third statement is **False**.

Thus, the correct statements are (i) and (ii).

### Summary of Results:
- **Correct Statements**: (i) and (ii)
- **Incorrect Statement**: (iii)