The sum of squares of deviations of a set of values about the mean is :

Options

A. zero
B. maximum
C. least
D. none of these

Answer

To find the sum of squares of deviations of a set of values about the mean, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Deviation**:
- The deviation of each value \( x_i \) from the mean \( \mu \) is given by \( (x_i - \mu) \).

2. **Calculating the Sum of Squares of Deviations**:
- The sum of squares of deviations is calculated as:
\[ \text{Sum of squares of deviations} = \sum (x_i - \mu)^2 \]
- Here, \( \sum \) denotes the summation over all values in the dataset.

3. **Using the Formula**:
- The formula for the sum of squares of deviations can also be expressed as:
\[ \sum (x_i - \mu)^2 = \sum x_i^2 - n\mu^2 \]
- Where \( n \) is the number of values in the dataset.

4. **Interpreting the Result**:
- The sum of squares of deviations is always non-negative because squaring any real number (the deviation) results in a non-negative value.
- The minimum value of the sum of squares of deviations occurs when all values are equal to the mean, which results in zero.

5. **Conclusion**:
- Therefore, the sum of squares of deviations of a set of values about the mean is always greater than or equal to zero, and it is zero only when all values are the same.

### Final Answer:
The sum of squares of deviations of a set of values about the mean is **greater than or equal to zero**, and it is zero when all values are identical.

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