CBSE2026Class Class 10 · Mathematics5 Marks · Long✅ Verified
The mean of the following frequency distribution is 35. Find the values of $x$ and $y$, if the sum of frequencies is 25: Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70; Frequency: 1, x, 5, 7, y, 3, 1
✅ Answer & Solution
Mid-points ($x_i$): 5, 15, 25, 35, 45, 55, 65; $f_i$: 1, x, 5, 7, y, 3, 1. Sum of frequencies: $1+x+5+7+y+3+1=25 \Rightarrow x+y+17=25 \Rightarrow x+y=8$ ...(i). $\Sigma f_ix_i = 1(5)+x(15)+5(25)+7(35)+y(45)+3(55)+1(65) = 5+15x+125+245+45y+165+65 = 605+15x+45y$. Mean $=\frac{\Sigma f_ix_i}{\Sigma f_i}$. $35=\frac{605+15x+45y}{25}$. $875=605+15x+45y$. $15x+45y=270$. $x+3y=18$ ...(ii). Subtracting (i) from (ii): $2y=10 \Rightarrow y=5$. From (i): $x=8-5=3$. Hence, $x=3$ and $y=5$.
