There are n sets of observations given as 1 , 2 ,3 , 4 ,5 , 6 , 7 ,8 , 9 ,10 , . . . . . The mean of the 1 3 t h set of observations is equal to

Step-by-step solution

In the n t h set of observation, the total observations are ‘ n ’ and the first observation of n t h set is 1 + 2 + 3 + . . . . + n - 1 + 1 = n - 1 n 2 + 1 = a Sum of all the n observations in the n t h set = n 2 2 a + n - 1 d = n 2 2 n - 1 n 2 + 1 + n - 1 = n 2 n 2 - n + 2 + n - 1 = n n 2 + 1 2 Mean = n n 2 + 1 2 n = n 2 + 1 2 Hence, for n = 13 Mean = 1 3 2 + 1 2 = 170 2 = 85