Question

the median of the following observation arranged in the ascending order is 24 .The observation are 14, 18, x + 2, X + 4,30,34. find the value of x + 2, x + 4 . find mean also​

Answer 1

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

Given observations are: 14, 18, x + 2, x + 4, 30, 34.

So, the total number of observations = 6. Also, the median of the above observation is 24.

24 = $\sf{\dfrac{ (\frac{6}{2})th \:term + ( \frac{6}{2}+1)th\: term }{2}}$

24 = $\sf{\dfrac{3th \:term + 4th\: term}{2}}$

24(2) = 3th term + 4th term

From above observations, we have 3th term = x + 2 and 4th term = x + 40

Substitute the values

⇒ 48 = x + 2 + x + 4

⇒ 48 = 2x + 6

⇒ 48 - 6 = 2x

⇒ 42 = 2x

⇒ x = 21

We have to find the value of (x +2) and (x + 4). So,

x + 2 = 21 + 2 = 23

x + 4 = 21 + 4 = 25

Now,

Mean = $\sf{\frac{Sum\:of\:all\:observations}{Total\:number\:of\:observations}}$

= (14 + 18 + 23 + 25 + 30 + 34)/6

= 114/6

= 24

Answer 2

||✪✪ GIVEN ✪✪||

• Median of 14, 18, (x + 2) , (x + 4) , 30, 34 are 24 .

|| ★★ FORMULA USED ★★ ||

The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest.

→ If there is an odd number of terms, the median is the center term. = (n+1)/2

→ If there is an even number of terms, add the two middle terms and divide by 2 = {(n/2 th term)+(n/2+1) th term}/2

|| ✰✰ ANSWER ✰✰ ||

In Ascending order :- 14, 18, (x + 2) , (x + 4) , 30, 34 = 6 Terms = Even Number .

So,

→ Median = {(n/2 term)+(n/2+1) term}/2

→ Median = {(6/2 term)+(6/2+1) term}/2

→ Median = {(3rd Term + 4th Term) /2 }

→ Median = { (x + 2) + (x + 4) } / 2

→ Median = (2x + 6)/2

→ Median = 2(x + 3)/2

→ Median = (x + 3)

So,

→ 24 = (x + 3)

→ x = 24 - 3

→ x = 21.

Hence,

→ x + 2 = 21 + 2 = 23 .

→ x + 4 = 21 + 4 = 25.

______________________

Mean :- ( Sum of Observation) / (Total Number of Observation ).

→ Mean = (14 + 18 + 23 + 25 + 30 + 34) / 6

→ Mean = 144 / 6

→ Mean = 24 .

Hence , The Required Mean is 24.

____________________________