11. In a survey of 260 dancers, 172 knew the ballroom dances, 145 knew the Latin dances, and 102 knew the swing dances. Of these, 65 knew the ballroom and swing dances, 93 knew the ballroom and Latin dances, and 56 knew the Latin and swing dances. Thirty-one dancers indicated that they knew all three styles of dance.
Create a Venn diagram to reflect the above data, label your diagram clearly and submit to the W1: Assignment 4 Dropbox. Use your diagram to answer the following questions here.
(a) How many knew only the ballroom dances?
(b) How many knew only the swing dances?
(c) How many knew exactly two of the three dances?
(d) How many knew the Latin and swing dances, but not the ballroom dances?
(e) How many knew none of these dances
I'll get you started.
Draw three intersecting circles. Label one B, one S and one L.
From the data given we can place 31 in the intersection of all three.
We are told 65 knew the ballroom and swing dances, therefore the number that know ballromm and swing only is 65-31=34
Similary the number that know swing and latin only is 56-31=25
And the number that know latin and ballroom only is 93-21=62.
Thus the number that know ballroom only is 172-(34+31+62)=54
Thus the number that know swing only is 102-(34+31+25)=12
Thus the number that know swing only is 145-(25+31+62)=27
The number that knew two of the three dances is
62+34+25=121
How many knew the Latin and swing dances, but not the ballroom dances is
12+25+27=64
Total number that knew all three is
45+34+12+31+62+25+27=236
so the how many knew none of these dances is 260-236=24
I hope this makes sense without a diagram. Please check the maths!
To answer the questions based on the given data, we can follow a step-by-step approach. Let's go through each question one by one:
(a) How many knew only the ballroom dances?
To find the number of people who knew only ballroom dances, we need to determine the count of people in the ballroom dances circle who are not in any other circles. This can be done by subtracting the counts of people who know more than one style of dance from the total count of people who know ballroom dances.
Hence, the number of people who knew only the ballroom dances is: 172 - 65 - 93 + 31 = 45.
(b) How many knew only the swing dances?
Similarly, to find the number of people who knew only the swing dances, we need to determine the count of people in the swing dances circle who are not in any other circles. This can be done by subtracting the counts of people who know more than one style of dance from the total count who know swing dances.
Hence, the number of people who knew only the swing dances is: 102 - 65 - 56 + 31 = 12.
(c) How many knew exactly two of the three dances?
To find the count of people who knew exactly two of the three dances, we need to add up the counts of people who know two styles of dances (ballroom and swing, ballroom and Latin, Latin and swing) and subtract the count of people who know all three styles of dances.
Hence, the number of people who knew exactly two of the three dances is: 65 + 93 + 56 - 31 = 183.
(d) How many knew the Latin and swing dances, but not the ballroom dances?
To find the number of people who knew the Latin and swing dances but not the ballroom dances, we need to subtract the count of people who know all three styles of dances from the count of people who know the Latin and swing dances.
Hence, the number of people who knew the Latin and swing dances but not the ballroom dances is: 56 - 31 = 25.
(e) How many knew none of these dances?
To find the count of people who knew none of the dances, we need to subtract the count of people who know at least one style of dance from the total count of dancers.
Hence, the number of people who knew none of these dances is: 260 - (172 + 145 + 102 - 65 - 93 - 56 + 31) = 7.
Now, you have the answers to all the questions.