Question

Describe the meaning of the "bar", "hat", and "tilde" symbols above a variable.

Answer 1

These are some common symbols in Statistics.

1) Bar notation : a bar notation above a variable usually denotes the mean / average of the variable data set. Suppose i have scores of 3 students, say X₁ ,X₂ , X₃ then X bar, i.e., denotes the mean / average of the scores of students.

2) Hat notation : This notation denotes the estimate value of a variable/parameter . In statistics, we try to estimate the values of population parameters from the smaller samples drawn from the population. Sample mean, is the estimator of population mean. Hence if X : Population mean , then X hat, = sample mean. X bar is estimated value of .

3) Tilde notation : This usually denotes that the variable is an operator. Eg, the differential operator.