The formula for calculating the standard deviation of the distribution of sample means given by

A. $${\sigma _{\overline {{x_1}} - \overline {{x_2}} }} = \sqrt {\frac{{\sigma _1^2}}{{{x_1}}} + \frac{{\sigma _2^2}}{{{x_2}}}} $$

B. $${\sigma _{\overline {{x_1}} - \overline {{x_2}} }} = {\left( {\sigma _1^2 + \sigma _2^2} \right)^2}$$

C. $${\sigma _{\overline {{x_1}} - \overline {{x_2}} }} = \frac{{{{\left( {{x_1}} \right)}^2} + {{\left( {{x_2}} \right)}^2}}}{{{\sigma _1} + {\sigma _2}}}$$

D. $${\sigma _{\overline {{x_1}} - \overline {{x_2}} }} = {\left( {{\sigma _1} + {\sigma _2}} \right)^2}$$

Answer: Option A