Question

The mean and variance of 7 observations are 8 and 16 respectively If one observation 14 is omitted and $a$ and $b$ are respectively mean and variance of remaining 6 observation, then $a+3 b-5$ is equal to ______

Answer 1

The correct answer is 37.
7x1​+x2​+…+x7​​=8
7x1​+x2​+x3​…+x6​+14​=8
⇒x1​+x2​+….+x6​=42
∴6x1​+x2​….+x6​​=642​=7=a
7Σxi2​​−82=16
Σxi2=560
⇒x12​+x22​+…+x62​=364
b=6x12​+x22​+….+x62​​−72
=6364​−49
b=670​
a+3b−5=7+3×670​−5
=37