Question

if the observations 19,24,27,28,X+2,35, 38,42,43 are in ascending Order and their Median Is 31 then what is the value X*

Answer 1

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Median=26

Observations 10,17,22,x+2,x+4,20,36,40

Median=

2

x+2+x+4

2

2x+6

=26

2x+6=52

2x=46

x=23

Answer 2

$\large\underline{\sf{Solution-}}$

Given set of observations are

$\rm :\longmapsto\:19,24,27,28,X+2,35, 38,42,43$

are arranged in ascending order.

and

Further, given that

Median is 31.

Now,

Number of observations = 9 [ odd ].

We know,

$\red{ \boxed{ \sf{ \:Median = {\bigg[\dfrac{n + 1}{2} \bigg]}^{th} \: observation}}}$

So, on substituting the values,

n = 9

Median = 31

$\rm :\longmapsto\: 31 = {\bigg[\dfrac{9 + 1}{2} \bigg]}^{th} \: observation$

$\rm :\longmapsto\: 31 = {\bigg[\dfrac{10}{2} \bigg]}^{th} \: observation$

$\rm :\longmapsto\: 31 = {\bigg[5 \bigg]}^{th} \: observation$

$\rm :\longmapsto\: 31 = X + 2$

$\bf\implies \:X = 29$

Additional Information :-

If n is even then

$\red{ \boxed{ \sf{ \:Median =\dfrac{1}{2} \bigg(\bigg[\dfrac{n}{2} \bigg]^{th} \: observation + {\bigg[\dfrac{n + 2}{2} \bigg]}^{th} \: observation\bigg)}}}$