Question

Which could be a conditional relative frequency table ???

Answer 1

Answer:

The table that represents the conditional relative frequency is:

                           A                B                Total

C                        0.25           0.75             1.0

D                        0.35           0.65             1.0

Total                 0.30           0.70              1.0

Step-by-step explanation:

We know that a conditional relative frequency table is one:

In which the entries in each row is divided by the row total .

                        OR

In which the entries in each column is divided by the column total.

i.e. the frequency or quantity of an item is being compared either to row or to the column total.

Hence, from the given options, the table that represent the conditional relative frequency is:

                           A                B                Total

C                        0.25           0.75             1.0

D                        0.35           0.65             1.0

Total                 0.30           0.70              1.0

 

Answer 2

The $\text{\bf second table}$ is conditional relative frequency table.

Further explanation:  

Conditional relative frequency is determined based upon a row or column. It is the ratio of a frequency in the center of the table to the frequency’s row total or column total. In the conditional relative frequency table, the “total” column will sum to $1$.

The given tables represent the different conditional probability.

Therefore, the sum of the conditional probability is $1$ in their column.

In the first frequency table, the sum of the total column can be calculated as follows:

$\boxed{1+1=2}$

The total probability of the conditional relative probability cannot be greater than $1$.

Therefore, Table 1 (attached in the end) is not the conditional relative frequency table.

In the second frequency table, the sum of the “total” column can be calculated as follows:

$\boxed{0.50+0.50=1}$

The total probability of the conditional relative probability is $1$.

Therefore, Table 2 is the conditional relative frequency table.

In the third frequency table is, the sum of the total column can be calculated as follows:

$\boxed{1+1=2}$

The total probability of the conditional relative probability cannot be greater than $1$.

Therefore, Table 3 is not the conditional relative frequency table.

Thus, Table 2 is the only conditional relative frequency table.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Probability

Keywords: Probability, ratio, row, column, total column, marginal frequency, joint frequency, distribution, sum, possible outcomes, event, two way table.