Question

can mean of data be negative?justify your answer.

Answer 1

Standard deviation can not be negative because it is square rooted variance. Let me explain this: 
Variance is calculated by summing all the squared distances from the mean and dividing them by number of all cases. So if one data entry in calculating variance is negative, it will always become positive when squared. 
And finally, when we square root the variance to get standard deviation, it must be a positive number because square root of positive number is always a positive number.

I hope this helps you.

Answer 2

Answer:

You can use the standard deviation then to design a confidence interval for all data points or even your model. ... Hence Standard deviation cannot be negative. Here (x-mean) is squared, so, this cannot be negative, N, number of terms cannot be negative, hence SD cannot be negative