Question

Angad was conducting an experiment in which the average of 11 observations came to be 90, while the average of first five observations was 87, and that of the last five was 84. What is the measure of the 6th observation?

• A. 145
• B. 150
• C. 165
• D. 135

Answer 1

The Correct Option is D

Let the sum of all 11 observations be \(S\). 
The average of 11 observations is 90, so:
\(S = 11 \times 90 = 990\)
Let the sum of the first five observations be \(S_1\) and the sum of the last five observations be \(S_2\). 
The average of the first five is 87, so:
\(S_1 = 5 \times 87 = 435\)
The average of the last five is 84, so:
\(S_2 = 5 \times 84 = 420\)
The sum of the 6th observation \(x_6\), the one we are looking for, is:
\(S = S_1 + S_2 + x_6\)
Substitute the known values:
\(990 = 435 + 420 + x_6\)
\(\Rightarrow\;\)\(x_6 = 990 - 435 - 420 = 135\)

Thus, the 6th observation is 135.