The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations in this data is replaced by , then the mean and variance become 10.1 and 1.99, respectively. Then + equals

Step-by-step solution

n=10 , mean =10 , variance =2 . So x_i = 100 and x_i^2 = 10(2+100)=1020 . After replacing by : new mean =10.1 x_i - + = 101 - = 1 New variance =1.99 x_i^2 - ^2 + ^2 10 - (10.1)^2 = 1.99 x_i^2 - ^2 + ^2 = 10(1.99+102.01) = 1040 ^2 - ^2 = 1040 - 1020 = 20 ( - )( + ) = 20 1 ( + ) = 20 + = 20