Average height and variance of $5$ students in a class is $150$ and $18$ respectively. If we add one student whose height is $156\ cm$ then new variance is

The initial sum of squares of heights can be found using the variance formula: Variance = (Sum(x^2)/n) - (Mean)^2. With n=5, mean=150, and variance=18, Sum(x^2) = 5 * (18 + 150^2) = 112590. Adding a student with height 156, the new sum of squares is 112590 + 156^2 = 136926, and the new mean is (5*150 + 156)/6 = 151. The new variance is (136926/6) - 151^2 = 22821 - 22801 = 20.