Present the given information in a venn diagram

Question

A survey was conducted to find out consumer preference of three types of media: newspapers, radio and television. The researcher surveyed 520 people. He found out that 340 listen to radio for news, 180 read newspapers and 150 watches the Television. 80 read the newspaper and listen to Radio, 85 read the newspaper and watch television, 35 listen to radio and watch Television and 25 utilize none of the three media

Present the given information in a venn diagram.

Determine the number that used all the three sources of news

Answer 1

Three interlocking circles represent the three media sets. Label them N (newspapers), T (television), R (radio). The people surveyed is a larger circle completely enclosing the others. There are 8 separate regions, caused by the interlocking circles and the region between the interlocking circles and the large surrounding circle.

a. N only

b. T only

c. R only

d. N and T only

e. T and R only

f. N and R only

g. All 3

h. None

Radio set: cefg=340; TV set: bdeg=150; newspaper set: adfg=180; N&R: fg=80; N&T: dg=85; R&T: eg=35; none: h=25. (cefg means c+e+f+g, etc., the total of the numbers of people in the regions.)

From these:

abcdefg=520-25=495; ad=100; af=95; be=65; ce=260; bd=115; c=495-adbefg=495-245=250; e=10; b=55; g=25; d=60; a=40; f=55. So (a,b,c,d,e,f,g)=(40,55,250,60,10,55,25,25). Therefore, g=25 is the number using all 3 sources.