Data Question ?

Question

A survey of 10281 people restricted to those who were either female or Hispanic or over 16 years of age, produced the following data:

Female: 5822
Hispanic female: 1745
Hispanic: 3490Over 16 and female: 859
Over 16: 4722
Over 16 and Hispanic: 1341
Hispanic female over 16: 239

Is the data consistent? If not, why?

Answer 1

Yes, the data appears to be consistent.

None of the boundaries are exceeded in any of the catagories, and based on the type of survey done, and who it was targeted at - it seems valid.

Answer 2

It's helpful to draw a Venn diagram here. That way you can separate out how many people fall into each section.

In the section for all people who are Hispanic, female, and over 16, there will be 239 people.

The section with people who are Hispanic and female, 239 are over 16, so the other 1745-239 = 1506 are under 16.

The section with people who are Hispanic and over 16, 239 are female, so the other 1341-239 = 1102 are male.

The section with people who are female and over 16, 239 are Hispanic, so the other 859-239 = 620 are not Hispanic.

The section with people who are Hispanic, 1102 are over 16 and male, 1506 are female and under 16, and 239 are over 16 and female, so 3490-1102-1506-239 = 643 are male and under 16.

The section with people who are female, 1506 are Hispanic and under 16, 620 are not Hispanic and over 16, and 239 are Hispanic and over 16, so 5822-1506-620-239 = 3457 are not Hispanic and under 16.

The section with peopl who are over 16, 1102 are Hispanic and male, 620 are female and not Hispanic, and 239 are female and Hispanic, so 4722-1102-620-239 = 2761 are not Hispanic and not female.

So add up these sections and you get the total number of people in the survey. 239 + 1506 + 1102 + 620 + 643 + 3457 + 2761 = 10328 total people in the survey. So no, the data is not consistant since there are more than 10281 people in the survey.

Answer 3

No.

Obviously Hispanic females are a subset of Females and Hispanics, etc.

We need to calculate how many people are in each subset exclusively, i.e. how many females are not over-16 and Hispanic, etc.

I can't reproduce the Venn diagrams here, but see if you can follow me:

OHF = 239 (i.e. over-16 Hispanic females)
HF = 1745 -239 = 1506 (i.e. under-16 Hispanic females)
HO = 1341 - 239 = 1102 (i.e over-16 Hispanic males)
OF = 859 - 239 = 620 (i.e. over-16 non-Hispanic females)
F = 5822 - 1506 - 620 - 239 = 3457 (i.e. under-16 non-Hispanic females)
H = 3490 - 239 - 1102 -1506 (i.e. under-16 Hispanic males)
O = 4722 - 239 -1102 - 620 (i.e. over-16 non-Hispanic males)

Total is 10328 not 10281.