Concept:If x1, x2, x3, ¦xn are the number of observations with respective frequencies f1, f2, f3, ¦ fn, thenThe sum of observations = f1x1 + f2x2 + f3x3 + ¦.+ fnxn.The total number of observations = f1+ f2+¦ + fn.Therefore, the mean of the data, x? = (f1x1+ f2x2 + f3x3 + ¦.+ fnxn) / ( f1+ f2+¦ + fn).The mean of the data, x? = \(\displaystyle ?\frac{f_ix_i}{N} \)Calculation:If the frequency of each class is doubled, thenTotal frequency = 2 ×120 = 240x? = \(\displaystyle ?\frac{f_ix_i}{N} \)? x? = \(\displaystyle \frac{f_1x_1+f_2x_2+f_3x_3+f_4x_4+f_5x_5}{N}\)? x? = \(\displaystyle \frac{2×17×10+2×(p+q)×30+2×32×50+2×(p-3q)×70+2×19×90}{2×120}\)? x? = \(\displaystyle \frac{17×10+(p+q)×30+32×50+(p-3q)×70+19×90}{120}\)? x? = \(\displaystyle \frac{100p \ - \ 180q \ +\ 3480}{120}\)Substituting the value of p and q in the above equation.? x? = \(\displaystyle \frac{100\times27 \ - \ 180\times 1 \ +\ 3480}{120}\)? x? = 50 ? The mean remains the same i.e. 50.