A random sample M1, M2,M3...M8 is taken from a population with unknown mean x. For each of the following, state wether or not it is a statistic, giving your reasons:
a) (M3+M8)/2
b) (Summation of Mi)/n
(Summation of Mi)/n is an approximation of the mean, much better than the first.
So a is not a statistic and b is.
https://www.jiskha.com/questions/1814615/a-random-sample-m1-m2-m3-m8-is-taken-from-a-population-with-unknown-mean-x-for-each-of
A statistic is a numerical value calculated from a sample that provides information about a population. Let's analyze each option:
a) (M3+M8)/2
This is a statistic because it is calculated using values from the sample (M3 and M8). It is used to estimate or provide information about an unknown parameter (in this case, the mean x of the population).
b) (Summation of Mi)/n
This is not a statistic. It represents the average value of the sample (the summation of all sample values divided by the sample size, n), which is also known as the sample mean. While it provides some information about the sample, it does not directly estimate or give insights into the population parameter (mean x). Therefore, it is not considered a statistic.