Given: The average height of a certain number of students in a group is 155.6 cm. 12 students having an average height of 150.5 cm join the group 7 students having an average height of 159 cm leave the group The average height of the students in the group will decrease by 34 mm i.e. 3.4 cm Concept used: Let xn be the observations and wn be the weights of the observations; the formula of the weighted average is given below. W = (w1x1+ w2x2 + w3x3+ ... + wnxn) ÷ (w1 + w2 + w3 + .... + wn) Calculation: Let the intial number of students be P. So, total height of P students = (P × 155.6) cm Now, total height increased by = (12 × 150.5) = 1806 cm Then, total height decreased by = (7 × 159) = 1113 cm Now, the total change in height = (1806 - 1113) = 693 cm The final number of stundets = (P + 12 - 7) = (P + 5) According to the question, 155.6 × P + 693 = (155.6 - 3.4) × (P + 5) ⇒ P = 20 ∴ The number of students initially in the group was 20.