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The average of a ten numbers is 72.8. The average of the first six numbers is 88.5 and the average of the last five numbers is 64.4. If the 6th number is excluded, then what is the average of the remaining numbers?
1. 65.8
2. 66.5
3. 67
4. 66

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Correct Answer - Option 3 : 67

Given:

Average of 10 numbers is 72.8

Average of first 6 numbers is 88.5

Average of last five numbers is 64.4

Formula Used:

Average = Sum of all observations/Total number of observations

Calculations:

Average of 10 numbers is 72.8

⇒ 72.8 = Sum of all 10 numbers/10

⇒ Sum of all 10 numbers = 72.8 × 10

⇒ Sum of all 10 numbers = 728

Average of first 6 numbers is 88.5

⇒ 88.5 = Sum of first 6 numbers/6

⇒ Sum of first 6 numbers = 88.5 × 6

⇒ Sum of first 6 numbers = 531

Average of last five numbers is 64.4

⇒ 64.4 = Sum of last 5 numbers/5

⇒ Sum of last 5 numbers = 322

Sum of total 11 numbers = Sum of first 6 numbers + Sum of last 5 numbers

⇒ Sum of total 11 numbers = 531 + 322

⇒ Sum of total 11 numbers = 853

But Sum of 10 numbers is 728

Number 6 is counted twice,

⇒ Number 6 = 853 – 728

⇒ Number 6 = 125

Now number 6 is excluded ,

⇒ New sum = 728 – 125

⇒ New sum = 603

Average of remaining 9 numbers,

⇒ Average = Sum of 9 numbers/ 9

⇒ Average = 603/9

⇒ Average = 67

∴ The average remaining 9 numbers is 67. 

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