Row 1st Column Blank 2nd Column Variable 1 left-parenthesis dollar sales right-parenthesis colon 3rd Column 48 22 50 2nd Row 1st Column Blank 2nd Column Variable 2 left-parenthesis number of movies right-parenthesis colon 3rd Column 3 1 2 EndLayout"/>
Then the data matrix is
with three rows and two columns.
We now present some descriptive statistics. We will begin with the mean vectors.
3.3 Mean Vectors
Let be random variables, where denotes the transpose of a matrix. The expected value of the random vector is defined as the vector of expectations i.e.
More generally, if is a matrix of random variables, then the is the matrix of expectations with elements , i.e.:
For a random vector , the mean vector consists of the means of each variable:
where . For example let be measurements on the first variable. Then the sample mean for the first variable is defined as follows:
The sample mean can be computed from the measurements on each of the variables. Therefore, in general for sample means, we have:
