Question

if the mode is 19.5 find p and q .If the class intervals are from 0-6 to 24-30 are continous and the frequencies are 7,p,10,12,q total=40​

Answer 1

Answer:

p=5 and q=6

Step-by-step explanation:

Mode=19.5

Modal class= 18-24

$l=18\\ h=6\\ f_{1}=12\\ f_{0}=10\\ f_{2}=q\\ \\ mode \: = \: l+\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}×h\\ \Rightarrow 19.5 \: = \: 18+\frac{12-10}{2×12-10-q}×6\\ \Rightarrow 19.5-18 \: = \: \frac{2×6}{24-10-q}\\ \Rightarrow 1.5(14-q) \: = \: 12\\ \Rightarrow 14-q \: = \: \frac{12}{1.5}\\ \Rightarrow 14-q \: = \: 8\\ \Rightarrow q \: = \: 14-8\\ \Rightarrow q \: = \: 6\\ \\ \sum_{}^{}f_{i} \: =\: 40\\ \Rightarrow 7+p+10+12+q\: =\: 40\\ \Rightarrow 29+6+p\: =\: 40\\ \Rightarrow 35+p\: =\: 40\\ \Rightarrow p\: =\: 40-35\\ \Rightarrow p\: =\: 5$