‘There are 10 numbers in a list. The first 9 numbers have a mean 6 and variance 2. The 10th number is 3. Find the mean and variance of all 10 numbers.
Let the mean of X be denoted by X’. (don’t know how to put the bar on top)
X’ = ∑X / 9 =6
So ∑X = 54
Hence new mean = (54+3) / 10 = 5.7
The issue I’m having is with the standard deviation.
s.d. = √(∑X² / n) - µ²
2 = √(X² / 9) – 36
360 = X²
So new s.d. = √ (360 + 3²) / 10) – 5.7² = 2.1
However the answer is 2.61---- anybody know why?
Let the mean of X be denoted by X’. (don’t know how to put the bar on top)
X’ = ∑X / 9 =6
So ∑X = 54
Hence new mean = (54+3) / 10 = 5.7
The issue I’m having is with the standard deviation.
s.d. = √(∑X² / n) - µ²
2 = √(X² / 9) – 36
360 = X²
So new s.d. = √ (360 + 3²) / 10) – 5.7² = 2.1
However the answer is 2.61---- anybody know why?