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The average of 16 numbers is 68.5 If two numbers 54 and 37 are replaced by 45 and 73 and one more number x is excluded, then the average of the numbers decreases by 1.5. The value of x is:
1. 111
2. 109
3. 118
4. 120

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Correct Answer - Option 3 : 118

Given:

Average of 16 numbers is 68.5

54 and 37 are replaced by 45 and 73

Concept Used:

Average = Sum of all observations/Total number of observations

Calculation:

Sum of all observations = Average × Total number of observations

⇒ Sum of all observations = 68.5 × 16

⇒ Sum of all observations = 1096

54 and 37 are replaced by 45 and 73

⇒ 54 + 37 = 91 replaced by 45 + 73 = 118

91 is replaced by 118, and one more number, i.e. x is excluded

⇒ 118 – 91 = 27 and x is added to the total sum 

New Sum = 1096 + 27 – x

⇒ New Sum = 1123 – x,

The average is decreased by 1.5

New average = 68.5 – 1.5

⇒ New average = 67

Total numbers = 16 – 1

⇒ Total numbers = 15

New sum of all observations = 67 × 15

⇒ New sum of all observations = 1005

⇒ x = New Sum –Sum

⇒ x = 1123 – 1005

⇒ x = 118

∴ The value of x is 118. 

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