how to combine standard deviations and mean for each group?

I have a table with 10000 rows, each row having 10 columns and their numbers vary from 0 to 80.Now, if I want to compare the mean of these rows.Maybe because of the largeness of one of the numbers in the row and the compensation of the smaller numbers of the same row, I can not make a fair comparison (because the value of each column is also important to me).

I know that I can use standard deviation. But I want to use a method that combines standard deviation and mean for each row to have just one number so I can sort the rows based on those rows.

I want to find the best rows. The best rows for me are the rows with the smallest Sd and at the same time the largest average.

• Welcome to the site. I don't think this can be answered without knowing what the data is and why you want to compare the rows Jan 17 '19 at 7:07
• I want to find the best rows. The best rows for me are the rows with the smallest Sd and at the same time the largest average. Jan 17 '19 at 7:12
• This is unorthodox, but you could do $\dfrac{\hat{\mu}}{\hat{\sigma}}$ to get 1 score out of each row. Jan 17 '19 at 8:33

When you want to find the "best" of something based on two or more measures, you have to decide how you want to weight them. There are all sorts of ways you could combine mean and sd into one measure:

$$\frac{\mu}{\sigma}$$

$$\mu - k\sigma$$ (where k is some constant determined by you)

$$\mu + \frac{k}{\sigma}$$

$$\sqrt{\mu \frac{1}{\sigma}}$$ (the geometric mean)

Or probably some others I am not thinking of. Which one is best for you depends on what you want.