# Thread: Need help with a question:

1. ## Need help with a question:

Q) Suppose a sample consisting of n=12 different data values has a mean of 5. One of the data values is -4 and another is 4.

a) A student calculates the sample variance of this sample and claims that S(squared) = 7.2. Explain why this value is incorrect.

b) If the two value -4 and 4 are removed what is the mean of the remaining data values?

Would much appreciate any help, not so much just the answers, but also how i get to them and the formulas used.

Thanks.

2. Not to sure how to answer the first one as we don't know much about the data. I'm guessing it has something to do with 4 and -4 being samples.

For the second consider

$\frac{x_1+x_2+\dots+x_{12}}{12}=5$

so

$x_1+x_2+\dots+x_{12}=60$

now removing 2 data points -4 and 4 will not change the sum of all data points therefore you get

$x_1+x_2+\dots+x_{10}=60$

and dividing by 10

$\frac{x_1+x_2+\dots+x_{10}}{10}=6$

Yes still dont quite understand the first myself.

4. Originally Posted by Dogfighters
Q) Suppose a sample consisting of n=12 different data values has a mean of 5. One of the data values is -4 and another is 4.

a) A student calculates the sample variance of this sample and claims that S(squared) = 7.2. Explain why this value is incorrect.

b) If the two value -4 and 4 are removed what is the mean of the remaining data values?

Would much appreciate any help, not so much just the answers, but also how i get to them and the formulas used.

Thanks.
a) By definition,
$S^2 = \frac{\sum_{i=1}^{12} (X_i - \bar{X})^2}{11}$
so
$S^2 \geq \frac{((-4) -5)^2 + (4 - 5)^2}{11} \approx 7.45$