Question

The following table shows the marks of $15$ students in accounts and economics. Construct a bivariate frequency distribution table.

Marks In Accounts	$28$	$26$	$27$	$25$	$28$	$27$	$26$	$27$	$27$	$26$	$25$	$26$	$27$
Marks in Economics	$22$	$21$	$21$	$20$	$21$	$21$	$20$	$19$	$21$	$19$	$19$	$20$	$21$

Answer 1

Hint: In this problem we need to construct the bivariate frequency distribution table. We know that the bivariate frequency distribution table is the representation of each possible combination for the two categorical variables according to the given data. For this we will write the marks of accounts in row of the distribution table and the marks of economics in column of the distribution table. Now we will find the number of possible combinations for the elements in the distribution table and note them in the table.

Complete step by step answer:
Given data is

Marks In Accounts	$28$	$26$	$27$	$25$	$28$	$27$	$26$	$27$	$27$	$26$	$25$	$26$	$27$
Marks in Economics	$22$	$21$	$21$	$20$	$21$	$21$	$20$	$19$	$21$	$19$	$19$	$20$	$21$

The ascending order of the variables in the first row of the given data is
$25$, $26$, $27$, $28$.
The ascending order of the variables in the second row of the given data is
$19$, $20$, $21$, $22$.
Forming the frequency distribution table with $25$, $26$, $27$, $28$ as column elements and $19$, $20$, $21$, $22$ as row elements, then the distribution table will be

Marks in Accounts$\left( \to \right)$	$25$	$26$	$27$	$28$
Marks in Economics$\left( \downarrow \right)$
$19$
$20$
$21$
$22$

In the first row of the distribution table we have $25$ and in the first column we have $19$. So the combination of $25$ marks in accounts and $19$ marks in economics occurred only one time in the given data.

Marks In Accounts	$28$	$26$	$27$	$25$	$28$	$27$	$26$	$27$	$27$	$26$	$25$	$26$	$27$
Marks in Economics	$22$	$21$	$21$	$20$	$21$	$21$	$20$	$19$	$21$	$19$	$19$	$20$	$21$

In the first row of the distribution table we have $25$ and in the first column we have$20$. So the combination of $25$ marks in accounts and $20$ marks in economics occurred only one time in the given data.

Marks In Accounts	$28$	$26$	$27$	$25$	$28$	$27$	$26$	$27$	$27$	$26$	$25$	$26$	$27$
Marks in Economics	$22$	$21$	$21$	$20$	$21$	$21$	$20$	$19$	$21$	$19$	$19$	$20$	$21$

Similarly searching for each combination and filling the distribution table then we will get the distribution table as

Marks in Accounts$\left( \to \right)$	$25$	$26$	$27$	$28$
Marks in Economics$\left( \downarrow \right)$
$19$	$1$	$1$	$1$
$20$	$1$	$2$	$1$
$21$		$1$	$4$	$1$
$22$				$2$

Note: We need to take care while observing the given data since it is a bivariate frequency distribution table we need to observe for the combinations in the given data not for the occurrence of variables. After filling the distribution table we can check it by doing the sum of elements in rows and columns individually. That means

Marks in Accounts$\left( \to \right)$	$25$	$26$	$27$	$28$	Total
Marks in Economics$\left( \downarrow \right)$
$19$	$1$	$1$	$1$		$1+1+1=3$
$20$	$1$	$2$	$1$		$1+2+1=4$
$21$		$1$	$4$	$1$	$1+4+1=6$
$22$				$2$	$2$
Total	$1+1=2$	$1+2+2=4$	$1+1+4=6$	$1+2=3$	$15$

In the above table we can observe the sum of elements row wise and column wise is equal to the number of observations. Hence the no mistake in the distribution table.