Question

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.

29, 32, 48, 50, x, x+2, 72, 78, 84, 95.

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Answer 1

Answer:

x=62

Step-by-step explanation:

median=(x+x+2)/2=63

=>2x+2=126

=>2x=124

=>x=62

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Answer 2

Solution :

$\bigstar$ Firstly, arrange the observations in ascending order.

29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

If the number of observation (n) is even then formula of the median will;

$\boxed{\bf{Median=\frac{\bigg(\frac{n}{2}\bigg)^{th} + \bigg(\frac{n}{2} +1\bigg)^{th} observation }{2} }}}}$

A/q

$\longrightarrow\sf{63=\dfrac{\bigg(\cancel{\dfrac{10}{2}}\bigg)^{th} + \bigg(\cancel{\dfrac{10}{2}} +1\bigg)^{th}}{2} }\\\\\\\longrightarrow\sf{63=\dfrac{5^{th}+(5+1)^{th}}{2}} \\\\\\\longrightarrow\sf{63=\dfrac{5^{th} + 6^{th}}{2} }\\\\\\\longrightarrow\sf{63=\dfrac{x+x+2}{2}\:\:\bigg[\therefore 5^{th}\: term = x\: \: \&\: \:6^{th}\:term=x+2\bigg]}\\\\\\\longrightarrow\sf{63=\dfrac{2x+2}{2} }\\\\\\\longrightarrow\sf{63\times 2=2x+2}\\\\\longrightarrow\sf{126=2x+2}$

$\longrightarrow\sf{2x=126-2}\\\\\longrightarrow\sf{2x=124}\\\\\longrightarrow\sf{x=\cancel{124/2}}\\\\\longrightarrow\bf{x=62}$

Thus;

The value of x will be 62 .