152
Find the missing frequencies $p$ and $q$ in the following frequency distribution, when sum of frequencies is $40$ and mean is $19$:
Class: $0-5, 5-10, 10-15, 15-20, 20-25, 25-30, 30-35$
Frequency: $2, 5, 6, p, 10, q, 4$
Class: $0-5, 5-10, 10-15, 15-20, 20-25, 25-30, 30-35$
Frequency: $2, 5, 6, p, 10, q, 4$
Show SolutionHide Solution↓
Correct table (2 Marks)
$N = 40 \Rightarrow p + q + 2 + 5 + 6 + 10 + 4 = 40 \Rightarrow p + q = 13$ (1 Mark)
Mean $= A + h \frac{\sum f_i u_i}{\sum f_i}$
$19 = 17.5 + 5 \times \frac{2q}{40}$ (1 Mark)
$1.5 = 5 \times \frac{2q}{40} \Rightarrow 1.5 = \frac{10q}{40} \Rightarrow 1.5 = \frac{q}{4} \Rightarrow q = 6$ (1/2 Mark + 1/2 Mark)
$p + 6 = 13 \Rightarrow p = 7$
$N = 40 \Rightarrow p + q + 2 + 5 + 6 + 10 + 4 = 40 \Rightarrow p + q = 13$ (1 Mark)
Mean $= A + h \frac{\sum f_i u_i}{\sum f_i}$
$19 = 17.5 + 5 \times \frac{2q}{40}$ (1 Mark)
$1.5 = 5 \times \frac{2q}{40} \Rightarrow 1.5 = \frac{10q}{40} \Rightarrow 1.5 = \frac{q}{4} \Rightarrow q = 6$ (1/2 Mark + 1/2 Mark)
$p + 6 = 13 \Rightarrow p = 7$