The hotdog brand clusters seem to be an example of competitive positioning in marketing. Hotdog brands need to be able to compete with other brands either by being healthier or by being tastier. Any brands with mid-range levels of sodium and calories will be cornered out of the market on all sides.

Yes, that's a good point. Competitive positioning is an important aspect of marketing, and hot dog brands are no exception. Brands need to find a way to differentiate themselves from competitors and appeal to their target audience. In the case of hot dogs, some brands may choose to focus on health aspects, while others may focus on flavor and indulgence. This creates distinct clusters of brands with different value propositions, and as you mentioned, brands with mid-range levels of sodium and calories may struggle to find a place in the market.

This was very helpful for me, but I am a little confused on #2, could someone please explain to me?

The problem is categorizing the dots into either lower or higher participation. It is asking you to find the best fitting answer, but in this case, it is basically just true or false. The first answer choice says, "The states with lower participation typically had lower math scores." If you look at the graph, all the green dots, which represent lower participation, are higher on the y-axis. The y-axis' variable is test scores. This means this is untrue. The second choice says, "The states with lower participation typically had higher math scores." Check the graph again. The green dots are high on the y-axis, representing higher test scores. This statement is true.

why is the pizza box a square if the pizza is a circle but the pizza slice is a triangle?

The pizza box is square because it is easier and more efficient to manufacture, stack, and transport square boxes. A square box is also more space-efficient than a round box, which would require more material to make and take up more space. As for why the pizza is a circle, it is because a circle is the most efficient shape to hold the maximum amount of pizza on a given surface area. Finally, the pizza slice is cut into a triangle because it allows for even portions and is easy to hold and eat.

How is it that the state that has lower participation get a higher math grade, 20% of my grade is participation

To help clarify: 1) in this SAT data, "participation" means "participated in taking the SAT". So it's a percent of students who took the SAT out of the total number of students eligible to take the SAT. In this case, "participation" doesn't refer to how much they participated in school or class in general. 2) An easier way to understand why the lower-participation states did better on the SAT (which sounds counter-intuitive), it's easier to think of it from the point of view of the higher participation states... When you have a whole lot more students taking the SAT, you're going to have a whole lot more chances of that big group getting way different scores. And with a wider range of scores, the average has a chance of being pulled down by the lower scores. ---> A mini-example of this effect: you work on a small group project, your group studies together, you each get top-scores your individual parts of the project, so your group gets a high average score. But if the teacher averages the project grades for everybody in the class, some groups might not have studied as much as your group, so the class average might be at least a little lower than your group's average. Hope this helps!

Main content

Course: AP®︎/College Statistics > Unit 5

Lesson 1: Representing the relationship between two quantitative variables

Clusters in scatter plots

Google Classroom

Learn what a cluster in a scatter plot is!

What are clusters in scatter plots?

Sometimes the data points in a scatter plot form distinct groups. These groups are called clusters.

Consider the scatter plot above, which shows nutritional information for

16

brands of hot dogs in

1986

. (Each point represents a brand.) The points form two clusters, one on the left and another on the right.

The left cluster is of brands that tend to be

low in calories and low in sodium

The right cluster is of brands that tend to be

high in calories and high in sodium

Practice problems

To better wrap our minds around the idea of clusters, let's try a couple of practice problems.

Problem 1: Male and female fish

Adult male Lamprologus callipterus (a type of fish) are much bigger than their female counterparts. They weigh about

13

times as much. Also, while females reach a length of

6

centimeters, males reach a length of

15

centimeters.

Which of the plots shown below might describe measurements of a group of adult Lamprologus callipterus?

There will be a cluster of data points for the female fish and another cluster for the male fish.

The female cluster needs to be shorter in length and lower in weight in comparison to the males, so it will be in the lower left corner of the graph.

The male cluster needs to be longer in length and higher in weight in comparison to the females, so it will be in the upper right corner of the graph.

Graph C is the only possible choice that matches the description of the fish.

Problem 2: SAT test scores

Some high school students in the U.S. take a test called the SAT before applying to colleges. The scatter plot below shows what percent of each state's college-bound graduates participated in the SAT in

2009 - 2010

, along with that state's average score on the math section.

There is a cluster of states with

lower participation

, and a cluster of states with

higher participation

What is the best interpretation of these clusters?

Why do clusters exist in data?

Explaining why clusters exist in a particular data set can be difficult. This article presented three data sets, each using data from the real world. Only in the fish data set was there a clear explanation behind the clusters.

If you have a theory that explains the clusters in either of the other data sets, please share your thoughts in the comments below.

Want to join the conversation?

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Pranu
Posted a year ago. Direct link to Pranu's post “I think that for the SAT ...”
I think that for the SAT problem, clusters might be present because in the states with lower participation because only the students that feel like taking the SAT is "worth it" or have confidence in their abilities take the test. This theory makes sense because of the math scores being higher for the students in states with lower participation. I'm not sure if this is really the reason, but I gave this a shot!
Button navigates to signup pageComment on Pranu's post “I think that for the SAT ...”
(75 votes)
Answer
Bella St.
Posted 4 years ago. Direct link to Bella St.'s post “The ingredients in the ho...”
The ingredients in the hot dogs can effect their ratings
Button navigates to signup pageButton navigates to signup page
(20 votes)
Answer
- arial_romero
  Posted 3 months ago. Direct link to arial_romero's post “`yummy !`”
  yummy !
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  (2 votes)
israelo64
Posted a year ago. Direct link to israelo64's post “anyone else on a chromebo...”
anyone else on a chromebook?
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(10 votes)
Answer
- Ella <3
  Posted a year ago. Direct link to Ella <3's post “i am go rtms”
  i am
  go rtms
  Button navigates to signup page
  (5 votes)
Edwin Sweeney
Posted 8 months ago. Direct link to Edwin Sweeney's post “The cluster on the top le...”
The cluster on the top left in SAT score probably has mostly east coast states lmaooo
Button navigates to signup pageComment on Edwin Sweeney's post “The cluster on the top le...”
(11 votes)
Answer
weirderquark
Posted 2 years ago. Direct link to weirderquark's post “The hotdog brand clusters...”
The hotdog brand clusters seem to be an example of competitive positioning in marketing. Hotdog brands need to be able to compete with other brands either by being healthier or by being tastier. Any brands with mid-range levels of sodium and calories will be cornered out of the market on all sides.
Button navigates to signup pageButton navigates to signup page
(9 votes)
Answer
- TotallyNotAFurryÒwÓ
  Posted a year ago. Direct link to TotallyNotAFurryÒwÓ's post “Yes, that's a good point....”
  Yes, that's a good point. Competitive positioning is an important aspect of marketing, and hot dog brands are no exception. Brands need to find a way to differentiate themselves from competitors and appeal to their target audience. In the case of hot dogs, some brands may choose to focus on health aspects, while others may focus on flavor and indulgence. This creates distinct clusters of brands with different value propositions, and as you mentioned, brands with mid-range levels of sodium and calories may struggle to find a place in the market.
  Button navigates to signup page
  (4 votes)
23kghamman
Posted 6 years ago. Direct link to 23kghamman's post “This was very helpful for...”
This was very helpful for me, but I am a little confused on #2, could someone please explain to me?
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- Hamilton, Michael - P3
  Posted 6 years ago. Direct link to Hamilton, Michael - P3's post “The problem is categorizi...”
  The problem is categorizing the dots into either lower or higher participation. It is asking you to find the best fitting answer, but in this case, it is basically just true or false.
  
  The first answer choice says, "The states with lower participation typically had lower math scores." If you look at the graph, all the green dots, which represent lower participation, are higher on the y-axis. The y-axis' variable is test scores. This means this is untrue.
  
  The second choice says, "The states with lower participation typically had higher math scores." Check the graph again. The green dots are high on the y-axis, representing higher test scores. This statement is true.
  Comment on Hamilton, Michael - P3's post “The problem is categorizi...”
  (11 votes)
Jojo
Posted a year ago. Direct link to Jojo's post “again, why?=”
again, why?=
Button navigates to signup pageComment on Jojo's post “again, why?=”
(7 votes)
Answer
undying-tonne39
Posted a year ago. Direct link to undying-tonne39's post “why is the pizza box a sq...”
why is the pizza box a square if the pizza is a circle but the pizza slice is a triangle?
Button navigates to signup pageComment on undying-tonne39's post “why is the pizza box a sq...”
(3 votes)
Answer
- TotallyNotAFurryÒwÓ
  Posted a year ago. Direct link to TotallyNotAFurryÒwÓ's post “The pizza box is square b...”
  The pizza box is square because it is easier and more efficient to manufacture, stack, and transport square boxes. A square box is also more space-efficient than a round box, which would require more material to make and take up more space. As for why the pizza is a circle, it is because a circle is the most efficient shape to hold the maximum amount of pizza on a given surface area. Finally, the pizza slice is cut into a triangle because it allows for even portions and is easy to hold and eat.
  Button navigates to signup page
  (7 votes)
Gage Davis
Posted 4 years ago. Direct link to Gage Davis's post “also some dont make a lot...”
also some dont make a lot sense like the college SAT's
Button navigates to signup pageComment on Gage Davis's post “also some dont make a lot...”
(4 votes)
Answer
- JamesonChunHeiW
  Posted a year ago. Direct link to JamesonChunHeiW's post “There is college sat's ∞”
  There is college sat's ∞
  Button navigates to signup page
  (3 votes)
edenkellywilkinson
Posted 5 years ago. Direct link to edenkellywilkinson's post “How is it that the state ...”
How is it that the state that has lower participation get a higher math grade, 20% of my grade is participation
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- B
  Posted 5 years ago. Direct link to B's post “To help clarify: 1) in th...”
  To help clarify:
  1) in this SAT data, "participation" means "participated in taking the SAT". So it's a percent of students who took the SAT out of the total number of students eligible to take the SAT. In this case, "participation" doesn't refer to how much they participated in school or class in general.
  
  2) An easier way to understand why the lower-participation states did better on the SAT (which sounds counter-intuitive), it's easier to think of it from the point of view of the higher participation states... When you have a whole lot more students taking the SAT, you're going to have a whole lot more chances of that big group getting way different scores. And with a wider range of scores, the average has a chance of being pulled down by the lower scores.
  ---> A mini-example of this effect: you work on a small group project, your group studies together, you each get top-scores your individual parts of the project, so your group gets a high average score. But if the teacher averages the project grades for everybody in the class, some groups might not have studied as much as your group, so the class average might be at least a little lower than your group's average.
  
  Hope this helps!
  Button navigates to signup page
  (3 votes)