Question

Numbers 50,42,35,2x+10,2x-8,12,11,8 are written in descending order and their median is 25,find x I will mark each and every person brainlliest who answers me

Answer 1

Answer:

The median of a set of observations is the middle term.

IF NUMBER OF OBSERVATIONS IS ODD:

We can straight away find out the median after arranging in descending/ascending order.

IF NUMBER OF OBSERVATIONS IS EVEN:

First we arrange the data in descending/ascending order and then find out the mean of the middle two numbers.

⇒ DESCENDING ORDER:

50, 42, 35, 2x+10, 2x-8, 12, 11, 8

We can see that the number of observations is even. So we calculate the mean of the middle two numbers and we will get our median.

MIDDLE TWO TERMS:

2x+10, 2x-8

Median= 25 (given)

⇒ 2x+10+2x-8/2= 25

4x+2= 25×2

4x= 50-2

4x= 48

x= 12

So, the value of x= 12

VERIFY:

2x+10

2(12)+10

24+10= 34

2x-8

2(12)-8

24-8= 16

NOW WE SUBSTITUTE THE VALUES OF THESE TERMS IN OUR DATA:

50, 42, 35, 34, 16, 12, 11, 8

NOW, WE FIND THE MEAN OF MIDDLE TWO TERMS:

34+16/2

= 50/2

= 25 (which matches our answer)

LHS=RHS

Hence, verified

Hope it helps

Please mark my answer as BRAINLIEST

Answer 2

$\rule{300}2$

Your Answer:

Given:-

• Numbers 50,42,35,2x+10,2x-8,12,11,8 are written in descending order
• Median is 25

To find:-

• Value of x

Solution:-

Total number of Observation = 8

So, even number of Observation

For even observation

$\tt Median = \dfrac{\dfrac{n}{2}th \ term + (\dfrac{n}{2}+1)th \ term}{2}$

So, finding n/2

$\tt \star \dfrac{n}{2} = \dfrac{8}{2} = 4 \\\\\\ \star \dfrac{n}{2}+1 = 4+1 = 5$

So, replacing values

$\tt Median = \dfrac{4th \ term + 5th \ term}{2} \\\\ \tt \Rightarrow 25 = \dfrac{2x+10 +2x-8}{2} \\\\ \tt \Rightarrow 25 \times 2 = 4x+2 \\\\ \tt \Rightarrow 50 = 4x+2 \\\\ \tt \Rightarrow 48 = 4x \\\\ \tt \Rightarrow \dfrac{48}{4} = x \\\\ \tt \Rightarrow 12=x$

So, value of x = 12

More to know

If the observation is odd,

$\tt Median = \dfrac{\dfrac{(n+1)}{2}th \ term }{2}$

$\rule{300}2$