Question

Hey Mates...
________________________

Please answer the question given in the attachment with full explanation...
________________________

NO SPAM....​

Answer 1

Q 6. Solution :-

$\begin{tabular}{|c|c|}\cline{1-2}Class Interval&Frequency\\\cline{1-2} 0-6&4\\\cline{1-2}6-12&x\\\cline{1-2}12-18&5\\\cline{1-2}18-24&y\\\cline{1-2}24-30&1\\\cline{1-2}\end{tabular}$

Calculating the C.F :-

$\begin{tabular}{|c|c|c|}\cline{1-3}Class interval&Frequency&C.F.\\\cline{1-3} 0-6&4&4\\\cline{1-3}6-12&x&4+x\\\cline{1-3}12-18&5&9+x\\\cline{1-3}18-24&y&9+x+y\\\cline{1-3}24-30&1&10+x+y\\\cline{1-3}&\sum f=20& \\\cline{1-3}\end{tabular}$

◘ 10 + x + y = 20

⇒  x + y = 20 - 10

⇒  x + y = 10          . . . (i)

◘  Median = 14.4  

So, Median class is 12 - 18

Now,

• Lower limit of the Median Class, l = 12
• Class width, h = 6
• Cumulative frequency of the class before the Median Class, cf = 4 + x
• n/2 = 20/2 = 10
• Frequency of the Median Class, f = 5

We know,

$\displaystyle{\sf{Median = l+\frac{\frac{n}{2}-cf }{f}\times h }}$

$\displaystyle{\sf{\implies Median =12+\frac{10-(4+x)}{5} \times6}}\\\\\displaystyle{\sf{\implies 14.4 =12+ \frac{6-x}{5} \times 6 }}\\\\\displaystyle{\sf{\implies 14.4 = 12+\frac{36-6x}{5} }}\\\\\displaystyle{\sf{\implies 14.4 = \frac{60+36-6x}{5} }}\\\\\displaystyle{\sf{\implies 72 =96-6x }}\\\\\displaystyle{\sf{\implies 12=16-x }}\\\\\boxed{\boxed{\sf{\implies x=4}}}$

Putting the value of x in eq. (i) :-

$\sf{x + y = 10}\\\\\sf{ \implies 4 + y = 10}\\\\\sf{\implies y = 10 - 4}\\\\\boxed{\boxed{\sf{\implies y = 6}}}$

Answer 2

Given :

• The median of the distribution is 14.4

• Total frequency is 20.

To Find :

• Find the value of x and y.

Solution:

$\boxed{\begin{array}{cccc}\sf Class\: interval&\sf Frequency&\sf C.F\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 0-6&\sf 4&\sf 4 \\\\\sf 6-12 &\sf x &\sf 4 + x \\\\\sf 12-18&\sf 5&\sf 9 + x\\\\\sf 18-24 &\sf y &\sf 9 + x + y\\\\\sf 24-30 &\sf 1 &\sf 10 + x + y\end{array}}$

Median = 14.4....(given)

So, Median class = 12-18

• Lower limit of median class (l) = 12

• Class interval (h) = 6

• CF = 4 + x

• Frequency of the median class = 5

• n/2 = 20/2 = 10

★$\large{\boxed{\green{\bf Median =\ l\ +\ \dfrac{\frac{n}{2}\ -\ cf}{f}\ \times\ h}}}$

➨$\sf 14.4 =\ 12\ +\ \dfrac{10 - (x + 4)}{5}\ \times\ 6$

➨$\sf 14.4 =\ 12 \ + \dfrac{6 \times (10 - x - 4)}{5}$

➨$\sf 12 = 36 - 6x$

➨$\sf 6x = 36 - 12$

➨$\sf 6x = 24$

➨$\pink{\sf x = 4}$

Now,

➨10 + x + y = 20

➨x + y = 10

➨y = 10 - 4.....(putting x = 4)

➨$\pink{\sf y = 6}$

Therefore, value of x and y are 4 and 6 respectively.