Question

the observation 20,24,29,x-3,x,x+1,50,are in adsending order find x if median is 38​

Answer 1

★ How to do :-

Here, we are given with seven observations and the median value of the same data. But, we are not given with the value of three observations in the given data, but it's replaced with a variable x. We are asked to find the value of that variable x. So, first we should find out the value in the given data which replaces with the value of median i.e, 38. So, we will use the formula of the median to find the value and later we can find the the value of x. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{n + 1}{2}th \: \: term}}}$

Substitute the value of n.

${\sf \leadsto \dfrac{7 + 1}{2}th \: \: term}$

Add the values in the numerator.

${\sf \leadsto \dfrac{8}{2}th \: \: term}$

Simplify the fraction to get the value.

${\sf \leadsto 4th \: \: term}$

Here, we can see that the fourth term of the data in ascending order is x-3. So, that can be considered as a median.

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Value of x :-

${\sf \leadsto x - 3 = 38}$

Shift the number 3 from LHS to RHS, changing it's sign.

${\sf \leadsto x = 38 - 3}$

${\sf \leadsto x = 35}$

$\Huge\therefore$ The value of x in the data is 35.