6th Grade - Statements Based On Data

 
     
 
     
 
Newsletters:
 
     
 
 
6th
Statistics
Statements Based on Data
Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
Identify claims made by data and conclusions. Understand that a claim is a conclusion drawn using the data that causes people to think in a certain way about the data. Evaluate the claims to determine if the are valid or invalid. Valid claims will have an unbiased (fair) sample, unbiased question and a solid data display. Invalid claims will have one or more of the following: biased (prejudiced) sample, biased question, or misleading data display. . Understand that biased questions cause misleading data. Biased questions give a prejudiced view of a topic or influence the sample group to answer in a specific way. Also, data displays can be misleading when the scale suggests changes or differences that are greater than they really are. Analyze the question and presentation of data to determine if it is misleading in any way. Determine of a data conclusion is biased (misleading or unfairly represents the target population) or representative (fairly represents the target population) based on both the question asked and data display. Understand that biased samples can cause misleading data, because they give a prejudiced view of a topic that is not representative of the entire population. Analyze how the data was collected and look for errors in sampling. Sampling errors include; choosing the wrong sample group or size and not including all parts of a target population. A biased survey does not fairly represent the entire population and at its results are often misleading. Use the information given about the data behind a claim to determine if the claim is valid or invalid.
 

Sample Problems

(1)

A group of people were given a survey about the state speed limit on open highways. The sample group included teenagers ranging in age from 14-19. After analyzing the data display, it was determined that 85% of the people would like the speed limit increased by 10 mph. Identify the claim and determine if it is valid or invalid.

(The claim is that 85% of people would like the speed limit increased by 10 mph. This is an invalid claim, because the sample is biased. They ages of the sample group were 14-19, this does not represent the general driving population.)

(2)

A survey was conducted by a department store to find the most popular shoe designer for 18-24 year olds. The store sent surveys out to all women on their mailing list within the age range. The data showed that the majority of 18-24 year olds prefer 4aDiva shoes. Is this claim valid? Explain.

(This claim is invalid. The survey was supposed to include all 18-24 year olds. Since men were excluded from the survey, the claim is invalid.)

(3)

The high school coach asked all the kids in his P.E. classes the following survey question. Is your favorite sport football? After disseminating his data, he concluded that football is the favorite sport of the majority of students at his school. What is his claim and is it valid? Explain.

(The claim is that most students at the coach’s school have football as a favorite sport. This claim is invalid for two reasons. First, the question the coach asked is biased. Secondly, the coach conducted a biased survey by only asking the kids in his P.E. class.)


(4)

Ben conducted a survey to determine the favorite after school snacks of students in his high school. He wrote up a survey asking, “What is your favorite after school snack?” He then received a list of all students and their homerooms. Ben randomly chose students from the list and sent the survey to their homerooms. After collecting the data he created the bar graph below. He concluded that the majority of boys have a snack favorite of chips, while the majority of the girls prefer fruit. Is this claim valid?

(This claim is valid, because the question and sample group are unbiased and the data display is solid.)

(5)

Ms. Redding looked at the data display and concluded that her school, Overachiever’s Elementary has test scores that are three times greater than Dullsville Elementary. Is her claim valid or invalid? Explain.


(Ms. Redding’s claim is invalid, because the data display is misleading. The scale does not start at zero. Her school actually only has 4 more points than Dullsville.)

Learning Tips

(1)

It is important that children are able to identify a claim made from a set of data. Be sure that your child understands that a claim is a statement that presents a viewpoint or an opinion. Many statements include the key words: likely, unlikely, somewhat likely, very likely, most, all, some, many, majority and minority. However, claims can also include a percentage or data statistic that has been founded through data collection. It will help the visual learner, if he/she gets into the habit of highlighting or underlining a claim. This will give him/her the ability to think critically about how the claim was made and whether or not it is valid.

(2)

The terms used to evaluate a claim are valid and invalid. A valid claim is conclusion that has been drawn from a good question, good sample and good data display. An invalid claim is an unsupported point of view. A claim can determined in valid if any part of the survey has not be conducted fairly. This includes the question, sample, and data display. You can play a game to be sure your child understands these terms. Use note cards or a piece of notebook paper cut in half. Write valid on one card and invalid on the next. Make simple statements like, “The sky is blue.” Have your child hold up the card that shows if your statement is valid (true, can be proven) or invalid (false). Be sure to have your child explain why he/she thinks your statements are valid or invalid.

(3)

Statistics are often reported in an effort to convince people of a point of view. The use of figures such as, tables, graphs and charts are intended to provide support for the point of view being portrayed. It is important to understand that flaws in research or even intentional data presentation can lead to false or unsupported claims being made. The nature of a survey question and data display can greatly influence data conclusions, or claims. It is most important to understand that the entire process of gathering and displaying data must be analyzed to ensure a fair representation has been made before drawing any conclusion or believing any claim. There are three main areas where statistics can go wrong: a biased question, a biased sample group, and a misleading data display. Each of these should be evaluated and by the data viewer, before drawing or believing any conclusion or point of view influenced by the data. When evaluating a data claim you may want to use the checklist below:

  • Unbiased question

  • Unbiased sample

  • Data display starts and zero and has even intervals

If you can check mark all three areas then it is justified to draw conclusions or determine that claims made are valid. However, if even one area is not checked, any conclusions drawn will be misleading and all claims made will be determined invalid.

(4)

It is crucial to understand the type of question asked when the data was gathered. There are two question types: biased questions and unbiased questions. Unbiased questions are fair; they don’t try to influence the person being interviewed in one way or another. Unbiased questions will give good answers that fairly represent the target population. Only surveys using these types of questions should be trusted and only claims made from this sort of question can be considered valid. An example of an unbiased question is, “What is your favorite sport?”. On the opposite end of the spectrum are biased questions. Children often confuse these new vocabulary terms and may need to use the statement “Biased is bad,” to help them remember. Biased questions can be considered bad because they try to influence the respondent’s answer. An example of a biased question would be, “Is volleyball your favorite sport?”. This question is biased because it is suggesting that volleyball is an answer. Biased questions will always try to lead the respondent to the answer the question writer wants. One way to do this is by suggesting an answer, such as in the question below. A second way to do this is to put pressure on the respondent so that he/she will answer in a particular way. For example, a question can be prefaced with a statement to make a respondent feel pressured to respond in a certain way. Here’s an example: “Teens across America voted Soccer as their favorite sport. What is your favorite sport?”. Finally, questions that produce strong reactions are biased. For example, in the question, “What should be done about students that bully others?”, the word bully creates a strong feeling or response. However, if the question were changed to “What should be done to students who are no kind to others?” reactions would not be as emotional or strong. Keep in mind that adjectives added to a question are a clear indicator of a biased question. Here’s an example, “Do you prefer delicious chocolate ice cream or vanilla?”. Help your child practice identifying words or phrases that might influence survey results. Then work together to suggest an alternative, neutral version of the question. This question suggests that the chocolate is delicious and that the vanilla is not. Claims that are based on data derived from a biased question should be determined invalid.

(5)

Only claims that are made based on data collected from an unbiased sample should be considered valid. In order for a sample to be unbiased, it must be representative of a population, give each member of a group an opportunity to be a part of the sample. Culture and gender are two biases that commonly cause sampling errors. In other words, if you’re asked to find the favorite radio station of 5th graders and you only ask girls, the boys are not being represented. Thus, you would need to include 5th grade boys and girls in your sample in order for your data to truly represent the group. Practice looking at different target populations (moms under 30, soccer players, PTA parents, etc…). Think about all the different kinds of people that are in each population. Some populations will have many different kinds of people, while others will have just a few. For example, if my target population was soccer players on The Hulks team, there would be boys ranging in age from 11-13. Also there would be the star players and the benchwarmers; however different, each of them is a part of the population. It is important that each type of person, age and sex is represented according to the target population. Make this real for your child by making diagrams or lists of people in the target population of his/her school or class. When evaluating a claim, determine if the sample is biased or unbiased before determining if the conclusion is valid or invalid. Biased samples will always have invalid claims, while unbiased samples can have valid claims so long as the question and data display aren’t misleading.

(6)

Misleading data displays lead to invalid claims. Data can be displayed in a variety of ways: line graphs, bar graphs, scatter plots, etc… There are three common errors that cause a misleading graph, which causes incorrect conclusions. The first is a graph with a scale that does not begin with a zero. Next, is a graph scale with uneven intervals with no real pattern (i.e. the scale counts as follows: 0, 1, 2, 4, 6). The third is missing categories (year, months, etc…). All data displays with any of the aforementioned problems will lead to invalid claims. However, valid claims can be determined by finding that the data display is sound with a proper scale, even intervals, and correct categories.

(7)

Make sure that all claims and their wording match the data. The wording of claims can be deceptive if you don’t think carefully about each word meaning and each part of the data display. For example, there may be a claim made it would be unlikely to see a boy snacking on vegetables when looking at the data display below. However, if you look closely at the data display, you will see that the over 125 boys do snack on vegetables. So a better claim would be that it is somewhat likely that you would see a boy snacking on vegetables.

Extra Help Problems

(1)

Which question is most fair? Explain.

  1. Should kids be forced to eat vegetables?

  2. Should kids eat vegetables?

  3. Should kids eat vegetables so that they can be healthier?

(Question B is the least biased, most fair. Question A included the word forced and people are likely to oppose being forced. Question C included the word healthier and people are likely to support being healthy. )

(2)

Which question is most fair? Explain.

  1. Do you prefer chocolate, vanilla or strawberry yogurt?

  2. Do you prefer delicious vanilla or chocolate or strawberry yogurt?

  3. Most kids prefer chocolate ice cream to vanilla or strawberry. Which is your favorite?

(Question A is the least biased, most fair. Question B included the adjective delicious to influence the respondent to support chocolate. Question C included a statement about what other kids prefer. This is likely to influence people to choose the preferred object. )

(3)

Which question is most fair? Explain.

  1. School violence has risen. Should teachers be allowed to check student backpacks?

  2. Children have the right to privacy. Should teachers be allowed to check student backpacks?

  3. Should teachers be allowed to check student backpacks?

(Question C is the most fair, because it is only question that allows people to give their own opinion without any persuasive viewpoints.)

(4)

Which question is least biased? Explain.

  1. Should kids be allowed to bring cell phones to school?

  2. Should young kids be allowed to bring disruptive cell phones to school?

  3. Should children be allowed to bring a cell phone to school in case there is an emergency?

(Question A is the least biased. Question B describes the children as young and the cell phones as disruptive. Question C influences people to support bringing the phone, by causing strong feelings when thinking about an emergency. )

(5)

Which question is the least biased? Explain.

  1. Are you in favor of helping others?

  2. Are you in favor of throwing more tax dollars at helping the homeless?

  3. Are you in favor of a tax increase to help the homeless?

(Question C is the least biased, most fair. Question A is too general and does not tell what exactly the survey is about. Question B uses the word “throw” which gives the impression that money is being thrown away. )

(6)

Highlight or underline the words that are causing a strong reaction to the question. Then, re-write the question so that it is unbiased.

Does wearing a helmet make bicycling safer?

(safer; Should bicyclists be forced to wear a helmet?)

(7)

Highlight or underline the words that are causing a strong reaction to the question. Then, re-write the question so that it is unbiased.

Should skateboarders be forced to wear a helmet and knee pads?

(forced; Should skateboarders wear a helmet and knee pads?)

(8)

Highlight or underline the words that are causing a strong reaction to the question. Then, re-write the question so that it is unbiased.

You would like to go to the park instead of bowling, wouldn’t you?

(You would like to; Would you like to go to the park or bowling?)

(9)

Highlight or underline the words that are causing a strong reaction to the question. Then, re-write the question so that it is unbiased.

Since state test scores are rising, should students be given less homework?

(state test scores are rising; Should students be given less homework?

(10)

Highlight or underline the words that are causing a strong reaction to the question. Then, re-write the question so that it is unbiased.

Do you prefer the bear or the stealth cheetah?

(stealth; Do you prefer the bear of the cheetah?)

(11)

Kristy randomly asked 25 students their favorite color. The table below shows the percentages chosen of each color. Using this table, Kristy concluded that orange was the color that students like the least. Is this claim valid? Explain.

Red

Blue

Green

Yellow

32

28

24

16

(Kristy’s claim is invalid. She did not ask students which color they liked the least. She asked them which color they liked the most. If she asked which color they liked the least, she would’ve gotten different answers.)

(12)

Kristy randomly asked 25 6th grade students their favorite color. The table below shows the percentages chosen of each color. Using this table, Kristy concluded that majority of 6th grade students prefer the color red. Is this a valid claim? Explain.

Red

Blue

Green

Yellow

32

28

24

16

(Kristy’s claim that that majority of the students prefer red is valid. It is valid because the question was unbiased and she took a random sample of 6th graders.)

(13)

Coach Taylor asked his football team their favorite school lunch. The table shows the tallies of each of the responses he got. Using the table, Coach Taylor concludes that the most popular school lunch is pizza. Is this a valid claim? Explain.

hamburger

pizza

tacos

ham sandwich

chicken salad

| | | |

| | | | | | | |

| | | |

| |

|

(Coach Taylor’s claim is invalid because his sample is biased. He only asked football players their favorite lunch, so it is misleading to use this data to claim that pizza is the most popular in all the school. The coach would need to change his sample so that it would fairly represent all students.)



(14)

Coach Taylor asked his football team their favorite school lunch. The table shows the tallies of each of the responses he got. Using the table, Coach Taylor concludes that the most popular school lunch is pizza. Re-write the c Coach Taylor’s claim to make it valid.

hamburger

pizza

tacos

ham sandwich

chicken salad

| | | |

| | | | | | | |

| | | |

| |

|

(The favorite lunch of the football team is pizza.)

(15)

Nadia surveyed the cheerleading team to find the preferred uniform style. She asked, “Do you prefer the classic, modern or hip hop uniform style?” She found that 12% of the team prefer classic, 58% prefer modern and 30% prefer hip hop. She concluded that most of the girls would prefer the modern uniform. Is this claim valid? Explain.

(Nadia’s claim is valid. She included all the cheerleaders, asked an unbiased question and read the data correctly in making her claim.)

(16)

Josh surveyed the basketball team to find the preferred basketball shoe. He asked the first 5 guys that showed up to practice what shoe they’d prefer to wear. Three guys preferred The Jump and two preferred The Beast. Josh concluded that the team’s preferred shoe is The Jump. Is this claim valid? Explain.

(Josh’s claim in not valid. His survey is biased because he only asked five team members what they thought. This is not enough to make a claim for the entire team. In addition, he only asked the first 5, which is a convenient sample, the least reliable.)

(17)

A group of people were given a survey about senior citizen discounts at the grocery store. The table below shows the percentages of people surveyed in different age groups that responded no. The survey question asked, “Should senior citizens discounts be raised to 25%?” The grocery store used the data to make the claim that their patrons don’t want the discount to be raised. Is this claim valid.

Ages

teens

20s-30s

40s-50s

50s-60s

70 & up

Percent

18%

35%

35%

8%

4%


(The store’s claim is invalid. This sample and display is biased because the people in their 50s and up only account for 12% of the total survey. Therefore, the sample does not represent their opinions adequately.)

(18)

A group of people were surveyed about their favorite presidential candidate. The results showed that 80% of the those surveyed were voting for the Republican candidate. The sample group included adults ranging in age from 45-56. The Republican party used the survey to make the claim that their candidate was in the lead. Is this claim valid.

(This claim is invalid, because the sample only included part of the voting population. It left out voters ranging in age from 18-44 and 57 and up.)

(19)

A radio station wants to survey its listeners to determine the favorite bumper sticker style. They announced that listeners could take an online survey to choose their favorite sticker style. 1,000 listeners went online and clicked on their favorite sticker. The radio station used the data to determine that their listeners prefer the new rock style. Is this valid? Explain.

(This claim is valid. The radio station opened the survey up to all listeners. Also, the question was unbiased since listeners just needed to look at the different styles and click on their favorite.

(20)

Marielle asked her classmates, “You’d prefer pepperoni pizza over sausage, wouldn’t you?”. She concluded that 86% of the students preferred pepperoni. Is her claim valid?

(No, the question Marielle asked is biased. She is leading her classmates to answer with pepperoni.)

(21)

Two different surveys were conducted to ask whether parents how they feel about school lunches. The table shows how the question was asked for each survey. Why did the surveys such different results? Explain how each question can cause a misleading claim.

Survey Question

Yes

No

Should students eat nutritious and well-balanced school lunches?

88%

12%

Should students be required to purchase school lunch?

33%

67%


(The first survey question influenced people with the used of the words nutritious and well-balanced. Since parents prefer their kids eat healthy, they would be influenced to respond yes, the majority did. The second survey also had a biased question. It used the word required, which will give a strong negative response by parents that prefer to control what their child eats. Since, neither survey is unbiased the results show the influence each question made on the people surveyed.)


(22)

Two different surveys were conducted to ask the favorite weekend hobby of sixth graders. What claims can be made about each of the surveys? Which of the surveys would gave misleading results? Explain.




Survey Question

Reading

Bike riding

Games

Sports

Which weekend hobby do you prefer?

18%


28%

33%

21%

Do you prefer playing games on the weekend or just reading, biking or playing the usual sports?


14%


16%


56%


14%


(The first survey shows that the most popular hobby is playing games, but they did not beat the others by a large extreme. The 6th graders that answered the second survey, were given a biased question, which led to misleading results. The question was written to influence people to choose games and a large majority of them did.)


(23)

6th graders were given the assignment to collect data regarding how many hours students spend on homework each night. Ryan wrote the survey question: Studies have shown that the brightest students spend at least one hour per night on homework. How much time to do you spend on homework each night?. He then surveyed all the boys and girls in his homeroom to collect his data. He found that that majority of students spend 1.25 hours on homework. Shauna wrote the survey question: How many hours per night do you spend on homework?. She then chose her friends as her sample group. Shauna claims that 6th graders spend 45 minutes on average completing homework nightly. Is either claim valid? Explain.

(Neither claim is valid. Ryan wrote a biased question. Shauna had a good, unbiased question, but a biased sample group.)

(24)

6th graders were given the assignment to collect data regarding how many hours students spend on homework each night. Raquel asked every other sixth grader on the class roster how long they spend on homework each night. She found that most 6th graders spend between 45 minutes and 1 hour on homework completion each night. Edmund asked each of the boys and girls in his after school program the same question. He found that 6th graders spend over an hour and a half completing homework. Which claim is more valid? Why?

(Raquel’s claim is more valid. She used a systematic by asking every other student on the class list of all 6th graders. This would give her a good overall view of the entire population. Edmund only asked the students in his after school program. This gives him a very narrow view of the topic.)

(25)

Assuming that the data below was collected with a random sample of teen in Huntington Beach, use the data table to make a valid claim about favorite summer sport(s) for teens in Huntington Beach and the least favorite.

Skateboarding

Surfing

Soccer

Volleyball

Tennis

36%

38%

4%

18%

4%

(Teen in Huntington Beach most enjoy surfing and skateboarding in the summer. They least enjoy soccer and tennis in the summer months.)


newsletters

 

Related Games

 
 

Copyright ©2009 Big Purple Hippos, LLC