The arithmetic mean and standard deviation of a data of nine numbers are 13 and 5 respectively. If 3 is included as the 10th item of the data, then the variance of the data of ten number is

Step-by-step solution

_ i=1 ^9 x_i 9 =13 _ i=1 ^9 x_i=117 . array rlrl & & & and & & ^2=25= _ i=1 ^9 x_i^2 9 -(13)^2 & _ i=1 ^9 x_i^2=9[25+169] array Now, after including 10^ th item as ' 3 ' gathered New mean y = _ i=1 ^9 x_i+3 10 = 117+3 10 =12 and new variance = ( _ i=1 ^9 x_i^2+9 ) 10 -(12)^2 = (169+25+1) 9 10 -144= 1755-1440 10 =31.5 gathered