# Thread: Unbiased Mean and Variance problem

1. ## Unbiased Mean and Variance problem

Hello~!! I'm new to this forum

Please show me how to do this little problem (from my A-level CIE stats book)-

Question:

Unbiased estimates of the mean and variance of a population, based on a random sample of 24 observations, are 5.5 and 2.42 respectively. Another random observation of 8.0 is obtained. Find new unbiased estimates of the mean and variance with this new information.

(the textbook says "8.0", but I think it should just be 8, but not too sure)

(the answer is Mean: 5.6 and Unbiased Variance: 2.569)

2. Originally Posted by agbrianlee355
Hello~!! I'm new to this forum

Please show me how to do this little problem (from my A-level CIE stats book)-

Question:

Unbiased estimates of the mean and variance of a population, based on a random sample of 24 observations, are 5.5 and 2.42 respectively. Another random observation of 8.0 is obtained. Find new unbiased estimates of the mean and variance with this new information.

(the textbook says "8.0", but I think it should just be 8, but not too sure)

(the answer is Mean: 5.6 and Unbiased Variance: 2.569)
Use $\displaystyle \bar{X} = \frac{\sum_{i=1}^n x_i}{n}$ as the unbiassed estimator of the mean.
When n = 24: $\displaystyle 5.5 = \frac{\sum_{i=1}^{24} x_i}{24} \Rightarrow \sum_{i=1}^{24} x_i = (24)(5.5) = 132$.