Question

Average of ‘n’ observations is 38, average of ‘n’ other observations is 42 and average of remaining ‘n’ observations is 55. Average of all the observations is:

• A. 45
• B. 35
• C. 55
• D. 40

Answer 1

Answer:

A. 45

Solution:

Given:

The average of ‘n’ observations is 38

The average of ‘n’ other observations is 42

The average of remaining ‘n’ observations is 55

Formula used:

${\rm{Average}} = {\rm{\;}}\frac{{{\rm{Sum\;of\;averages}}}}{{{\rm{Sum\;oftotal\;number}}}}$

Calculation:

Sum of first n observations = 38n

Sum of next n observations = 42n

Sum of last n observations = 55n

Total sum = 38n + 42n + 55n = 135n

Sum of total number = n + n + n

⇒ 3n

$Average = {\rm{\;}}\frac{{135n}}{{3n}}$

⇒ 45

∴ The Average of all the observations is 45