Question

For a grouped data L=239.5 n=50 cf=13 f=12and h=20 then find median​

Answer 1

Answer:

The median of the distribution is 259.5 units.

Step-by-step-explanation:

We have given the values of frequencies and class widths of a grouped frequency distribution.

We have to find the median of the distribution.

Now,

$\displaystyle{\bullet\sf\:Lower\:class\:limit\:of\:median\:class\:(\:L\:)\:=\:239.5}$

$\displaystyle{\bullet\sf\:Sum\:of\:frequencies\:(\:N\:)\:=\:50}$

$\displaystyle{\bullet\sf\:Cumulative\:frequency\:of\:the\:class\:preceding\:median\:class\:(\:c\:f\:)\:=\:13}$

$\displaystyle{\bullet\sf\:Frequency\:of\:median\:class\:(\:f\:)\:=\:12}$

$\displaystyle{\bullet\sf\:Class\:interval\:of\:medina\:class\:(\:h\:)\:=\:20}$

Now, we know that,

$\displaystyle{\pink{\sf\:Median\:=\:L\:+\:\left(\dfrac{\dfrac{N}{2}\:-\:c\:f}{f}\:\right)\:\times\:h}\sf\:\:\:-\:-\:[\:Formula\:]}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:\left(\dfrac{\cancel{\dfrac{50}{2}}\:-\:13}{12}\:\right)\:\times\:20}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:\left(\:\dfrac{25\:-\:13}{12}\:\right)\:\times\:20}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:\cancel{\dfrac{12}{12}}\:\times\:20}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:1\:\times\:20}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:20}$

$\displaystyle{\implies\boxed{\red{\sf\:Median\:=\:259.5\:units}}}$

The median of the distribution is 259.5 units.

Answer 2

Answer:

$\huge\mathfrak\red{\bold{\underline{☯︎{Lεศɢนε \: σʄ \: Mıŋɖร}☯︎ }}}$

$\huge\green{ \underline{ \boxed{ \sf{Given:}}}}$

• $\displaystyle{\bullet\sf\:Lower\:class\:limit\:of\:median\:class\:(\:L\:)\:=\:239.5}$

• $\displaystyle{\bullet\sf\:Sum\:of\:frequencies\:(\:N\:)\:=\:50}$

• $\displaystyle{\bullet\sf\:Cumulative\:frequency\:of\:the\:class\:preceding\:median\:class\:(\:c\:f\:)\:=\:13}$

• $\displaystyle{\bullet\sf\:Frequency\:of\:median\:class\:(\:f\:)\:=\:12}$

• $\displaystyle{\bullet\sf\:Class\:interval\:of\:medina\:class\:(\:h\:)\:=\:20}$

$\huge\green{ \underline{ \boxed{ \sf{To find:}}}}$

• The median of the distribution.

$\huge\green{ \underline{ \boxed{ \sf{Formula:}}}}$

$\displaystyle{\blue{\sf\:Median\:=\:L\:+\:(\dfrac{\dfrac{N}{2}\:-\:c\:f}{f}\:)\:\times\:h}}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:(\dfrac{\cancel{\dfrac{50}{2}}\:-\:13}{12}\:)\:\times\:20}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:(\:\dfrac{25\:-\:13}{12}\:)\:\times\:20}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:\cancel{\dfrac{12}{12}}\:\times\:20}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:1\:\times\:20}$

$\displaystyle{\implies\sf\:Median\:=\:239.5\:+\:20}$

$\displaystyle{\implies\boxed{\pink{\sf\:Median\:=\:259.5\:units}}}$

• The median of the distribution is 259.5 units.

$\huge\green{\boxed{\pink{\bold{\fcolorbox{orange}{yellow}{\orange{Hope\:It\:Helps༒}}}}}}$