An interesting use of the inclusion/exclusion rule is to check survey numbers for consistency. For example. suppose a public opinion polltaker reports that out of a national sample of 1,200 adults, 675 are married, 682 are from 20 to 30 years old, 684 are female. 195 are married and are from 20 to 30 years old, 467 are married females, 318 are females from 20 to 30 years old, and 165 are married females from 20 to 30 years old. Are the polltaker’s figures consistent? Could they have occurred as a result of an actual sample survey?

To find if the polltalkers figure are consistent or not and also, if that has occurred as a result of actual sample.

Given information:

An interesting use of the inclusion/exclusion rule is to check survey numbers for consistency. For example, suppose a public opinion polltaker reports that out of a national sample of 1,200 adults, 675 are married, 682 are from 20 to 30 years old, 684 are female, 195 are married and are from 20 to 30 years old, 467 are married females, 318 are females from 20 to 30 years old, and 165 are married females from 20 to 30 years old.

Concept used:

Let M represent the set of married people in the given sample.

Let Y represent the set of people between 20 and 30 in the sample.

Let F represent the set of females in the sample.

Calculation:

Then, the number of people less than or equal to the size of the sample is represented by MUYUF.

According to the given data,

N(M)=675N(Y)=682N(F)=684

The number of people who are married and between 20 and 30 years old is given by M∩Y.

∴N(M∩Y)=195

The number of people who are married and female is given by M∩F.

∴N(M∩F)=467

The number of people who are female from 20 to 30 years old is F∩Y