Question

For the bivariate frequency table for$x$ and$y$, then the marginal frequency distribution for$y$ is given by

$\raisebox{1ex}{$y$}\!\left/ \!\raisebox{-1ex}{$x$}\right.$	$0-10$	$10-20$	$20-30$	$30-40$	Sum
$0-10$	$3$	$2$	$4$	$2$	$11$
$10-20$	$-$	$1$	$3$	$1$	$5$
$20-30$	$3$	$2$	$-$	$-$	$5$
$30-40$	$-$	$6$	$7$	$-$	$13$
Sum	$6$	$11$	$14$	$3$	$34$

• A.

  $0-10$	$6$
  $10-20$	$11$
  $20-30$	$14$
  $30-40$	$3$

• B.

  $0-10$	$11$
  $10-20$	$5$
  $20-30$	$5$
  $30-40$	$13$

• C.

  $0-10$	$10$
  $10-20$	$12$
  $20-30$	$14$
  $30-40$	$1$

• D. None of these

Answer 1

The correct option is B

$0-10$	$11$
$10-20$	$5$
$20-30$	$5$
$30-40$	$13$

Step 1: Define the bivariate frequency and marginal frequency.

Bivariate frequency: A bivariate frequency distribution, in other words, is the frequency distribution of two variables. Bivariate data (Bi means “two” and “variate” means “variable”) is a term that represents data that is made up of observations that have two attributes or characteristics (2 variables).

Marginal frequency: Marginal frequency is the entry in the “total” for the column and the “total” for the row in the two-way frequency table. Marginal relative frequency is the sum of the joint relative frequencies in a row or column.

the marginal frequency distribution for$y$ is given by

$0-10$	$11$
$10-20$	$5$
$20-30$	$5$
$30-40$	$13$

Hence, option $\mathbf{\left(}\mathit{B}\mathbf{\right)}$ is the correct option.