Question

Find the values of x and y if the median of the following data is 31 ?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

$\begin{tabular}{|c|c|c|}\cline{1-3}\ \bigstar\:{\bf{Class}\: \bigstar}& \bigstar\:{\bf{frequency}\: \bigstar}& \bigstar\:{\bf{C.F.}\: \bigstar} \\ \cline{1-3}\ 0-10 & 5 & 5 \\ \cline{1-3}\ 10-20 & x & 5+x \\ \cline{1-3}\ 20-30 & 6 & 11+x \\ \cline{1-3}\ 30-40 & y & 11+x+y \\ \cline{1-3}\ 40-50 & 6 & 17+x+y \\ \cline{1-3}\ 50-60 & 5 & 22+x+y \\ \cline{1-3}\end{tabular}$

N = 22 + x + y = 40

x + y = 18 .........(1)

We know that,

$\huge{\boxed{\boxed{\green{\sf{Median = L + (\frac{\frac{N}{2} - C. F}{f} )\times h}}}}}$

Where,

L = 30, f = y, h = 10 and C. F = (11 + x)

$\sf{31 = 30 + ( \frac{20 - (11 +x)}{y} ) \times 10} \\ \\ \sf{1 = \frac{(9 - x)}{y} \times 10 } \\ \\ \sf{y = 90 - 10x} \\ \\ \sf{10x + y = 90}....(2) \\ \\ \bf{from \: equation \: 1} \\ \\ \sf{x = 18 - y} \\ \\ \bf{put \: value \: of \: x \: in \: equation \: 2} \\ \\ \sf{10(18 - y) + y = 90} \\ \\ \sf{180 - 10y + y = 90} \\ \\ \sf{ - 9y = 90 - 180} \\ \\ \sf{y = \frac{ \cancel{- 90}}{ \cancel{ - 9}} } \\ \\ \sf{y = 10} \\ \\ \large{ \boxed{ \orange{ \sf{y = 10}}}} \\ \\ \bf{put \: value \: of \: y \: in \: equation \: 1} \\ \\ \sf{x + 10 = 18} \\ \\ \sf{x = 8} \\ \\ \large{ \boxed{ \purple{ \sf{x = 8}}}}$