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 observations, then a+3b−5 is equal to
Explanation
Solution:
Pehle naya mean (a) nikaalte hain:
∑xold=7×8=56
∑xnew=56−14=42
a=642=7
Ab naya variance (b) nikaalte hain:
Old Variance: 7∑xi2−(8)2=16⟹7∑xi2=80⟹∑xi2=560
New ∑xi2=560−142=560−196=364
b=6364−(7)2=3182−49=3182−147=335
Final calculation:
a+3b−5=7+3(335)−5
a+3b−5=7+35−5=37
Explanation
Solution:
Pehle naya mean (a) nikaalte hain:
∑xold=7×8=56
∑xnew=56−14=42
a=642=7
Ab naya variance (b) nikaalte hain:
Old Variance: 7∑xi2−(8)2=16⟹7∑xi2=80⟹∑xi2=560
New ∑xi2=560−142=560−196=364
b=6364−(7)2=3182−49=3182−147=335
Final calculation:
a+3b−5=7+3(335)−5
a+3b−5=7+35−5=37
