Percentage increase between 2 Ven diagrams

BallisticWeasel

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Question 3

A survey based on 152 employees in the public sector, relating to their preferred automobile brand revealed the following: 98 employees prefer Lexus; 85 prefer Amarok; and 65 prefer Mercedes. 40 of them prefer Amarok and Mercedes; 42 prefer Lexus and Mercedes; 25 prefer Amarok only; 18 prefer Mercedes only.

Draw a Ven Diagram to illustrate this information (8 marks)
a) how many prefer Amarok and Lexus but not Mercedes? ( 2 marks)
b) how many preferred Amarok or Lexus but not Mercedes? ( 2 Marks)
c) How many preferred Lexus only? ( 2 Marks)
d) how many preferred all three brands? (2 marks)
e) whichis the greater number; those who prefer Lexus and Mercedes; or those who prefer Mercedes and Amarok; by what percentage is it greater? ( 4 marks)

Answers i got...
a) 20
b) 81
c) 36
d) 146
e)Lexus and Mercedes. 28.58%

3.2 In order to gain more insight on employeespreferences, twenty three (23) employees from the private sector were asked about automobiles of their preference. Five (5) of them dislike all three brands. Eight (8) preferred both Lexus and Mercedes. Another eight (8) of them preferred both Mercedes and Amarok. Four (4) of them preferred all three brands. Four (4) prefer Mercedes only. The remainder preferred Amarok only.

i) how many of the twenty three (23) employees prefer Lexus only ( 2Marks)
ii) How many of the twenty three (23) employees prefer Amarok only (2 Marks)
iii) From the total of one hundred and seventy five (175) employees from both the public and private sector, howmany employees disliked all three brands? ( 2 Marks)
iv) What is the percentage increase i. The number of employees who preferred all three brands? ( 4 Marks)
v) Compute the percentage decrease in the proportion of employees that prefer all three brands ( 5 Marks)

Answers i got.

i) 0
ii) 2
iii) 11
iv)?
v)?

Please help me underatand how to calculate iv and v. I am unsure of what is required.

Regards
 
Draw a Venn Diagram to illustrate this information (8 marks)
a) how many prefer Amarok and Lexus but not Mercedes? ( 2 marks)
b) how many preferred Amarok or Lexus but not Mercedes? ( 2 Marks)
c) How many preferred Lexus only? ( 2 Marks)
d) how many preferred all three brands? (2 marks)
e) whichis the greater number; those who prefer Lexus and Mercedes; or those who prefer Mercedes and Amarok; by what percentage is it greater? ( 4 marks)
...
3.2 In order to gain more insight on employeespreferences, twenty three (23) employees from the private sector were asked about automobiles of their preference. Five (5) of them dislike all three brands. Eight (8) preferred both Lexus and Mercedes. Another eight (8) of them preferred both Mercedes and Amarok. Four (4) of them preferred all three brands. Four (4) prefer Mercedes only. The remainder preferred Amarok only.

i) how many of the twenty three (23) employees prefer Lexus only ( 2Marks)
ii) How many of the twenty three (23) employees prefer Amarok only (2 Marks)
iii) From the total of one hundred and seventy five (175) employees from both the public and private sector, howmany employees disliked all three brands? ( 2 Marks)
iv) What is the percentage increase in[?] The number of employees who preferred all three brands? ( 4 Marks)
v) Compute the percentage decrease in the proportion of employees that prefer all three brands ( 5 Marks)

First, check your answers for d and e in the first question, and for b in the second.

As for iv and v, I don't even know for sure what they mean! A percentage increase requires some base to start with, and a change from that. We don't have two different surveys of the same group of people. It appears that they mean "from the public sector survey to the private sector survey", so they may mean "what is the percentage increase from the answer to 1d (which isn't 146!) to 4, but that doesn't really make sense, and even with the right numbers, it's not an increase. (It's like saying, "There are 7 men with red hair, and 6 women with red fair. What is the percentage increase in people with red hair?")

Then they want you to do the same thing with the percentages (or fractions) representing each of those numbers, which makes a little more sense, but still isn't really an increase or decrease.

Do you know how to find a percentage increase?
 
First, check your answers for d and e in the first question, and for b in the second.

As for iv and v, I don't even know for sure what they mean! A percentage increase requires some base to start with, and a change from that. We don't have two different surveys of the same group of people. It appears that they mean "from the public sector survey to the private sector survey", so they may mean "what is the percentage increase from the answer to 1d (which isn't 146!) to 4, but that doesn't really make sense, and even with the right numbers, it's not an increase. (It's like saying, "There are 7 men with red hair, and 6 women with red fair. What is the percentage increase in people with red hair?")

Then they want you to do the same thing with the percentages (or fractions) representing each of those numbers, which makes a little more sense, but still isn't really an increase or decrease.

Do you know how to find a percentage increase?
Good day Dr. Peterson.

Unfortunately i do not. Is it as simple as calculating the percentage difference between the two? As for my answer for d in the first question, the want to know how many preferred all three brands. I assume it is the number where all 3 circles intersect.? According to samples i have, when the say Lexus and Amarok, they mean the middle part between Lexus and Amarok but if the say Lexus or Amarok, they mean the complete total of Lexus, Amarok and the people that prefer both. Is this wrong?
 
Unfortunately i do not. Is it as simple as calculating the percentage difference between the two?
Yes, assuming you mean the right thing by "percentage difference"! Find the amount of change, and divide by the first amount.

As for my answer for d in the first question, the want to know how many preferred all three brands. I assume it is the number where all 3 circles intersect.? According to samples i have, when the say Lexus and Amarok, they mean the middle part between Lexus and Amarok but if the say Lexus or Amarok, they mean the complete total of Lexus, Amarok and the people that prefer both. Is this wrong?
Yes, this is the intersection. I think the number you gave is the union (the number who preferred any of the three brands, rather than all).
 
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