The standard deviaton of a data is ….. Of any change in origin but is …..of change of scale .

Explanation

To solve the question, we need to understand the concepts of standard deviation in relation to changes in origin and scale of a dataset.

1. **Understanding Changes in Origin**:
- When we talk about a change in origin, we refer to adding or subtracting a constant value to all data points in the dataset. For example, if we have a dataset and we add 5 to each data point, the mean and the standard deviation will change. However, the standard deviation will remain the same because it measures the spread of the data, which is not affected by a constant shift.

2. **Understanding Changes in Scale**:
- A change in scale refers to multiplying or dividing all data points by a constant value. For example, if we multiply each data point by 2, the spread of the data changes, and so does the standard deviation. In this case, the standard deviation is dependent on the scale of the data.

3. **Filling in the Blanks**:
- Based on the above understanding, we can fill in the blanks in the statement:
- The standard deviation of a data is **independent** of any change in origin but is **dependent** on the change of scale.

Thus, the complete statement is:
"The standard deviation of a data is independent of any change in origin but is dependent on the change of scale."