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# How to test consistency for data?

## Question:

In a survey of 500 persons, 300 were married and 250 were successful executives. 198 successful executives were married. Is the data consistent?

## Solution:

Step 1: Define the Attributes

• A = married

• α = unmarried

• B = successful attributes

• β = unsuccessful attributes

Step 2: Find the given frequencies with N

• N = 500

• (A) = 300

• (B) = 250

• (AB) = 198

Step 3: Prepare the 9 square table and find the missing frequencies

 ​ B ​β Total A 198 (A​β) = 102 300 α (αB) = 52 (α​β) = 148 250 Total (B) = 250 (​β) = 250 500

Both conditions below are satisfied for the above data. Hence the data is consistent.

1. Any class frequencies cannot be greater than total population for the data to be consistent. Hence each class frequency must be less than or equal to "N" for the data to be consistent.

2. Any class frequencies cannot be negative for the data to be consistent. Hence each class frequency must be greater than or equal to 0 for the data to be consistent.

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