Question

plz help solve fast ???? ​

Answer 1

$\sf\large\undeline{Given:}$

$\sf{\implies Mean=42}$

$\sf{\implies Total frequency=100}$

$\sf\large\undeline{To\:Find:}$

The value of missing frequency=?]

$\sf\large\undeline{Solution:}$

To calculate the missing frequency at first we have to make a table after that we have to calculate the value of x and y to calculate the value of x and y , we have to set up equation then solve.]

$\begin{array}{|c|c|c|c|} \cline{1-4} \sf CI & \sf f & \sf x & \sf fx \\ \cline{1-4} 0-10 & 7 & 5 & 35 \\ \cline{1-4} 10-20 & 10 & 15 & 150 \\ \cline{1-4} 20-30 & \sf X & 25 & \sf 25X \\ \cline{1-4} 30-40 & 13 & 35 & 455 \\ \cline{1-4} 40-50 & \sf Y & 45 & \sf 45Y \\ \cline{1-4} 50-60 & 10 & 55 & 550 \\ \cline{1-4} 60-70 & 14 & 65 & 910 \\ \cline{1-4} 70 - 80 & 9 & 75 & 675 \\ \cline{1-4} & \sf \sum\:f=63 + X + Y & & \sf \sum\:f\:x=2775 + 25X + 45Y \\ \cline{1-4} \end{array}$

By calculating we get here:]

$\sf{\implies \sum\:f\:x=2775+25x+45y}$

$\sf{\implies \sum\:f=63+x+y}$

$\sf{\implies setting\:up\: first\: equation:}$

$\sf{\implies Total\: frequency=63+x+y}$

$\sf{\implies 100=63+x+y}$

$\sf{\implies x+y=100-63}$

$\sf{\implies x+y=37-------(i)}$

$\sf{\implies setting\:up\:2nd\: equation:}$

To calculate 2nd equation we have to apply the formula of mean:]

$\tt{\implies Mean=\dfrac{\sum\:f\:x}{\sum\:f}}$

$\tt{\implies 42=\dfrac{2775+25x+45y}{63+x+y}}$

$\tt{\implies 2646+42x+42y=2775+25x+45y}$

$\tt{\implies 42x-25x+42y-45y=2775-2646}$

$\tt{\implies 17x-3y=129----(ii)}$

Now solving here , equation:]

In eq (I) multiplying by 17 the subtracting from eq (ii)

$\tt{\implies 17x+17y=629}$

$\tt{\implies 17x-3y=129}$

By solving we get , here]

$\tt{\implies 20y=500\implies y=25}$

Putting the value of y=25 in eq (i)]

$\sf{\implies x+y=37}$

$\sf{\implies x+25=37}$

$\sf{\implies x=37-25\implies x=12}$

$\sf\large{Hence,}$

$\sf\purple{\implies The\: missing\: frequency=25\:and\:12}$

Answer 2

refer the attachment :)