+1348 If a data set $\{a_1, a_2,\dots, a_n\}$ has arithmetic mean $x,$ then its variance is defined to be
\[\dfrac{(a_2-x)^{2} +(a_3 -x)^{2} +\dots+(a_n -x)^{2}}{n},\]
and its standard deviation is the square root of the variance. Krys replaces the number $6$ in the data set $\{1, 2, 3, 4, 5, 6\}$ with the positive number $B$ and notices that the new standard deviation is exactly five times the old standard deviation. What is the value of $B\,?$
