# 6th Grade - Statements Based On Data

## Building Blocks/Prerequisites

### 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.)

### Online Resources

 (1) (2) (3)

### 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.

(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?

(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.)