Question

The Median of 25, 38 ,55 ,x + 2 ,x + 6 ,65 , 72, 80 ,arranged in ascending order is 60 .Find the Missing terms .​

Answer 1

The missing terms are 58 and 62

Given :-

• The Median of 25,38,55,x + 2,x + 6,65, 72,80 arranged in ascending order is 60.

To find :-

• The missing terms.

Solution :-

Given observations are 25,38,55,x + 2,

x +6,65, 72,80

The data is in the ascending order.

Number of observations (n) = 8

We know that

If the number of observations is n, an even number then the median of the observation is the average of (n/2)th and [(n/2)+1]th observations.

n/2th observation = 8/2

= 4th observation

4th observation = x+2

[(n/2)+1]th observation = 4+1

= 5th observation

5th observation = x+6

Average of 4th and 5th observations

= (x+2+x+6)/2

= (2x+8)/2

= 2(x+4)/2

= (x+4)

The Median = (x+4)

According to the given problem

The Median of the data = 60

Therefore, x+4 = 60

=> x = 60-4

=> x = 56

The value of x = 56

If x = 56 then x+2 = 56+2 = 58

If x = 56 then x+6 = 56+6 = 62

Answer :-

→ The missing terms in the data are 58 and 62

Used formulae:-

→ If the number of observations is n, an even number then the median of the observation is the average of (n/2)th and [(n/2)+1]th observations.

Points to know :-

→ The middle term of the data when it is arranged either ascending order or descending order is called Median of the data.

→ If the number of ok observations is n , an odd number then the Median is

(n+1)/2 th observation.

→ Median is denoted by M .

→ Median is one of the measures of central tendency.

Answer 2

Given :

• Data = 25, 38 ,55 ,x + 2 ,x + 6 ,65 , 72, 80
• Median = 60

To Find :

• The Missing terms

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SolutioN :

☆ Formula Used :

• Median = Sum of two Middle terms/2

☆ Calculating the Value of x :

$➺ \qquad \; \sf{ Median = \dfrac{ Sum \; of \; Two \; Middle \; Terms }{ 2 } }$

$➺ \qquad \; \sf{ 60 = \dfrac{ \bigg( x + 2 \bigg) + \bigg( x + 6 \bigg) }{ 2 } }$

$➺ \qquad \; \sf{ 60 = \dfrac{ 2x + 8 }{ 2 } }$

• Cancelling 2x + 8 by 2 :

$\\ ➺ \qquad \; \sf{ 60 = x + 4 }$

$➺ \qquad \; \sf{ 60 - 4 = x }$

$\\ ➺ \qquad \; {\underline{\boxed{\pmb{\pink{\frak{ x = 56 }}}}}} \; {\green{\pmb{\bigstar}}}$

☆ Calculating the Missing Terms :

• ➳ x + 2 = 56 + 2 = 58
• ➳ x + 6 = 56 + 6 = 62

$\therefore \;$ The two Missing terms are 58 and 62 .

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