There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a testwhere, x is a positive integer. Find the mean and standard deviation of the marks.

First find x as given total number of students is 60 i.e.     x−2+x+x2+(x+1)2+2x+x+1    =60⇒    5x−2+x2+x2+1+2x+1    =60⇒    2x2+7x    =60⇒    2x2+7x−60    =0⇒    2x2+15x−8x−60    =0⇒    x(2x+15)−4(2x+15)    =0⇒    (2x+15)(x−4)    =0⇒    x=−152,x    =4⇒    x=4    (∵x is positive ) Mean x¯=ΣfixiN=16860=2.8∴  Variance σ2=Σfixi2N−(x¯)2=54660−(2.8)2 =9.1−7.84=1.26=1.12