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There are thirteen 2-digit consecutive odd numbers. If 39 is the mean of the first five such numbers, then what is the mean of all the thirteen numbers?

There are thirteen 2-digit consecutive odd numbers. If 39 is the mean of the first five such numbers, then what is the mean of all the thirteen numbers? Correct Answer    47

Given : 

There are thirteen 2-digit consecutive odd numbers.

39 is the mean of the first five such numbers.

Formula used :

Average = Sum of all observations/Number of observations 

Calculations :

Let the number be 2x + 1, (2x + 3), (2x + 5), ...........(2x + 25) 

According to the question 

(2x + 1 + 2x + 3 + 2x + 5 + 2x + 7 + 2x + 9)/5 = 39    (Average of the first five numbers)

x = 17 

So numbers are 35, 37, 39,  ..............59 

Average of all 13 numbers = (35 + 37 + 39 ..........+ 59)/13 

⇒ 611/13 

⇒ 47 

∴ The average of all numbers will be 47. 

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