No, it is not possible to obtain a negative value for either variance or standard deviation.
Variance is defined as the average of the squared differences from the mean. Since we are squaring the differences, the result is always non-negative. Even if all data points are the same, making the differences zero, the variance will be zero rather than negative.
Standard deviation, which is the square root of the variance, also cannot be negative. The square root of a non-negative number is always zero or positive. Therefore, both variance and standard deviation are always zero or positive values.
In summary, variance and standard deviation are measures of spread that can only be zero or positive, reflecting how data points deviate from the mean. Any assertion of a negative variance or standard deviation indicates a misunderstanding of these statistical concepts.