Question

The median of the following observations (arranged in ascending order) is 34 . Find the value of x and the value of third term. 18 , 26 , x + 3 , 30 , x + 8 , 35 , 37 , 38 , 40 , 41​

Answer 1

Answer:

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Step-by-step explanation:

The median of the following observations (arranged in ascending order) is 34 . Find the value of x and the value of third term. 18 , 26 , x + 3 , 30 , x + 8 , 35 , 37 , 38 , 40 , 41

Answer 2

The value of x is 25.

The third term is 28.

Step-by-step explanation:

Given:

• The median of the following observations (arranged in ascending order) is 34 .
• 18 , 26 , x + 3 , 30 , x + 8 , 35 , 37 , 38 , 40 , 41

To find:

• Find the value of x and the value of third term.

Solution:

Concept to be used:

• Arrange the data in ascending order.
• If number of terms(n) are odd, then median is $\left( \frac{n + 1}{2} \right) ^{th}$
• If number of terms (n) are even, then median is mean of $\left({ \frac{n}{2} }\right)^{th} \: and \: \left({ \frac{n}{2} + 1}\right)^{th}$terms.

Step 1:

Find the value of x.

As, numbers are already arranged in ascending order.

So,

Number of data(n)= 10

So,

18 , 26 , x + 3 , 30 , x + 8 , 35 , 37 , 38 , 40 , 41

Median is mean of 5th and 6th data.

5th data is x+8 and 6th data is 35.

$34 = \frac{x + 8 + 35}{2}$

or

$x + 43 = 68$

or

$x = 68 - 43$

or

$\bf x= 25$

Step 2:

Find the value of 3rd term.

Third term is x+3.

So,

put x=25

Third term is $25 + 3$

Third term is 28.

Thus,

Value of x is 25 and third term is 28.

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