I am getting difficulty in understanding the definition of the statistic.
From wikipedia, I come to understand that statistic is any 'information' (for example, range, mean, variance) of any sample of any given population.
Whereas in my college the definition of statistic is given as:
Suppose $(X_1, X_2,… ,X_i,…,X_n)$ is a random sample of size $n$ from any given PDF or PMF. A function $T=t(X_1, X_2,… ,X_i,…,X_n)$ free from unknown parameter is called a statistic.
I cannot understand the definition given in my college. Are the two definitions related to each other? What is the need of finding the statistic?
Best Answer
A statistic is a function of your data.
That's all it is. In different context, you may be interested in different statistics. Maybe T = number of observations. That's a valid statistic. Or T = max value observed. T = seventh observation. T = sixth largest observation. I guess it's valid to say T=1 too, just a constant, although it's quite meaningless. Most commonly as an introduction, we look at T = sample mean, and use it to infer the population parameter.
Maybe your samples aren't event real numbers! For example, maybe your X1, X2, ... are students first names. A valid statistic could be T= most common name. Or T = total number of characters in every name.
To reiterate, a statistic is just a function of your data. In introductory courses, you often work with sample means, sample variances, and play with some algebra to make a mathematical statement about a population's parameter.