A survey asked a group of people where they got their news: a newspaper, TV, or the Internet. The responses are recorded in the following table

Question

A survey asked a group of people where they got their news: a newspaper, TV, or the Internet. The responses are recorded in the following table.

Newspaper and TV- 46

TV only-20
Internet only- 12
Newspaper and Internet- 57
TV and Internet- 50
Newspapers- 75
TV and internet, but not newspapers- 19

All Three- 31

None of the three- 8


Using N for a newspaper, T for TV, and I for the Internet, make a Venn diagram for news sources. The completed diagram should give the number in each region of the diagram.

Answer the questions below:

(Fill in the blanks below and give all of your answers as whole numbers.)

How many people were surveyed?
How many people got their news from only one source?
How many people got their news from the Internet alone?
How many people got none of their news from TV?

Answer 1

Here is a rather crude attempt at a Venn Diagram:

 

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

     8 others

 

            N                                               T

                3                   15               20

 

                                     31

 

                        26                     19

 

                                      12

                                       I

 

Questions:

 

How many people were surveyed?  8 + 3 + 15 + 20 + 31  + 26 + 19 + 12 = 134

How many people got their news from only one source?  3 + 20 + 12  =  45

How many people got their news from the Internet alone?  12   (given)

How many people got none of their news from TV?  15 + 20 + 31 + 19 = 85

 

 

Answer 2

Adrienne,

 

The best way to answer your question would be to draw the Venn Diagram and label 1 circle "Newspapers", 1 circle " TV" and the last circle "Internet." Next, you would place the number of people for only TV (20) and only Internet (12). The space where all 3 circles interlock would be the space to put 31 since these people use all 3 media sources. Don't forget to put the number 8 outside of all circles since these people use none of the above sources. We know from the question that 50 people use both TV and Internet but we have already accounted for 31 people who use all 3 sources, so in the space where the TV and Internet circles interlock place 19 people (50-31=19). We also know 46 people use both Newspapers and TV. Again, we have accounted for 31 people so 46-31=15 people. Place this number in the interlocking space between Newspapers and TV. We have to do the same process for the interlocking space between Newspapers and Internet, so 57-31=26 people. Finally, 75 people use newspapers but the clue does not say the word only so we have to figure out how many people use only newspapers. Subtract all of the interlocking numbers from the total number of 75 people to solve. 75-15-31-26= 3 people

 

For the questions: 

How many people were surveyed?

You will want to add up all of the above numbers to get the total amount of people surveyed.

3+15+20+31+26+19+12+8 = 134 people

How many people got their news from only one source?

You will want to add up all of the people who use only newspapers, only TV, and only the Internet

3+20+12 = 35 people 

How many people got their news from the Internet alone?

You don't have to do any adding for this question. The question above tells you only 12 people get their news from Internet alone so the answer is 12 people.

How many people got none of their news from TV?

You will need to exclude anyone within the TV circle in your Venn Diagram since any people who use TV would be within the circle. However, make sure to add the 8 people who use other sources since they don't use TV either.

3+26+12+8 = 49 people