Question

estion 4
a) Numbers 50,42, 35, 2x + 10, 2x + 8, 12, 11, 8, 6 are written in descending order and
their median is 25, find x​

Answer 1

Answer:

3.5

Step-by-step explanation:

Number of observation, n= 9

Median = (n+1)/2 th observation

= (9+1)/2 th observation

= 10/2 th observation

= 5 th observation

25 = 2x+8

2x = 17

x = 3.5

Answer 2

★ How to do :-

Here, we are given with nine observations in which they are arranged in descending order. We are also given with the value of the median of this data. But, we are not given with two numbers, but we are given with some variables with equation. We are asked to find the value of that variable x. So, first we will find which of the following observations can be the median. For that we have some formulas which can be applied here. So, let's solve!!

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➤ Solution :-

Median :-

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

Substitute the value of n.

${\tt \leadsto \dfrac{9 + 1}{2} \: th \: term}$

Add the values in numerator and simplify the obtained fraction.

${\tt \leadsto \cancel \dfrac{10}{2} = 5th \: \: term}$

Here, we can see that the fifth term in this data is 2x + 8.

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Value of x :-

${\tt \leadsto 2x + 8 = 25}$

Shift the number 8 from LHS to RHS, changing it's sign.

${\tt \leadsto 2x = 25 - 8}$

Subtract the values on the RHS.

${\tt \leadsto 2x = 17}$

Shift the number 2 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{17}{2}}$

Simplify the fraction on RHS.

${\tt \leadsto \pink{\underline{\boxed{\tt x = 8.5}}}}$

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Verification :-

${\tt \leadsto 2x + 8 = 25}$

Substitute the value of x.

${\tt \leadsto (2 \times 8.5) + 8 = 25}$

Multiply the numbers in bracket.

${\tt \leadsto 17 + 8 = 25}$

Add the values on LHS.

${\tt \leadsto 25 = 25}$

So,

${\sf \leadsto LHS = RHS}$

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Hence solved !!

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Formulas :-

${\sf \longrightarrow {Median}_{(Even \: observations)} = \dfrac{n}{2} + 1 \: th \: \: term}$

${\sf \longrightarrow {Median}_{(Odd \: observations)} = \dfrac{(n + 1)}{2}th \: term}$