x bar represents sample mean then why is the answer choice 3?
why x bar is not 4.5 based on the formula it should be (1+3+5)/(3-1). Could you please explain this?
Hi Sahar!
Thanks for reaching out!
I assume that your confusion comes from the way we calculate the sample variance or standard deviation, where we divide by n−1.
The correct formula to calculate the mean of a set of numbers is the sum of all the numbers divided by the count of the numbers. In this case, to find the mean of 1, 3, and 5, you should sum these values and divide by 3 (the number of Johnny's friends), not by 3−1.
The numbers 1, 3, and 5 represent a sample from Johnny's class, not the entire population, as he only asked 3 of his friends. So, we'll be calculating the sample mean (x̄) and the sample standard deviation (s).
To find the sample mean, we calculate (1+3+5)/3 = 9/3, which gives 3.
The standard deviation is calculated as the square root of the variance. So, the variance is ((1−3)^2+(3−3)^2+(5−3)^2)/3-1, which is 8/2, or 4.
The sample standard deviation is the square root of the variance (4), which is 2.
Therefore, the correct answer to the quiz question is choice 3: x̄=3, s=2.
Hope this helps.
Best,
Ivan