A variable X takes values 0, 0, 2, 6, 12, 20, , n(n-1) with frequencies ^nC₀, ^nC₁, ^nC₂, ^nC₃, ^nC₄, ^nC₅, , ^nC_n , respectively. If the mean of this data is 60 , then its median is :

Step-by-step solution

The given variable X takes values x_r = r(r-1) with frequencies f_r = n r for r = 0, 1, 2, , n . The mean of the data is given by X = _ r=0 ^ n f_r x_r _ r=0 ^ n f_r . We know that _ r=0 ^ n f_r = _ r=0 ^ n n r = 2^n . The sum of the products is: _ r=0 ^ n f_r x_r = _ r=0 ^ n r(r-1) , n r Using the property r(r-1) , n r = n(n-1) , n-2 r-2 , we get: _ r=2 ^ n n(n-1) , n-2 r-2 = n(n-1) , 2^ n-2 Substituting these into the mean formula: X = n(n-1) , 2^ n-2 2^n = n(n-1) 4 Given that the mean is 60 : n(n-1) 4 = 60 n(n-1