Chapter 10.3, Problem 2E

To determine

Toexplain:

The comparison between the definitions of joint relative frequency, marginal relative frequency, andconditional relative frequency.

Answer to Problem 2E

• The ratio of a frequency which is not in the total row or the total column to the total number of values is called joint relative frequency.
• The sum of the joint relative frequencies in a given row or column is called marginal relative frequency.
• The ratio of a joint relative frequency to the marginal relative frequency is called conditional relative frequency.

Explanation of Solution

• Definition of joint relative frequency:

The ratio of a frequency which is not in the total row or the total column to the total number of values is called joint relative frequency.

i.e.

Consider,

Joint relative frequency = $JRF$

Frequency not in total row or total column = $FNTROC$

Total number of values = $TNV$

  $\therefore JRF=\frac{FNTROC}{TNV}$

• Definition of marginal relativefrequency:

The sum of the joint relative frequencies in a given row or column is called marginal relative frequency.

i.e.

Consider,

Marginal relative frequency = $MRF$

• Definition of conditional relative frequency:

The ratio of a joint relative frequency to the marginal relative frequency is called conditional relative frequency.

i.e.

Consider,

Conditional relative frequency = $CRF$

  $\therefore CRF=\frac{JRF}{MRF}$

Thus, above is the comparison of the joint relative frequency, marginal relative frequency, and conditional relative frequency.