6th Grade - Selecting A Sample

 
     
 
     
 
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6th
Statistics
Selecting a Sample
Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.
Understand that a sample is a survey that is taken by only looking at part of a population. A sample should only be used when surveying the population will be timely or costly. There are different types of samples that can be taken. Identify each of the different sample types required for sixth grade: convenience, random, and systematic. Understand that a convenience survey consists a of a sample group that already exists. Conducting a survey to find the most popular music amongst 6th graders and using the students in your homeroom would be an example of a convenience survey. Often times, convenience samples don’t represent the entire population and can make the survey biased. A biased survey does not fairly represent the entire population and at its results are often misleading. A random sample, however is the most reliable sample and will be the least biased of all sample types. A random sample best represents the entire population because all members of the population have an equally likely chance to be included in the survey, however only a set about will be chosen. An example of a random sample is the names of all students in a school being placed in a bucket and 50 names being drawn to choose the sample group. . A systematic sample is another fairly reliable sampling method. When a pattern is used to find the sample group, a systematic sample is being conducted. For instance, if a list of students from a school is printed and every 10th student is interviewed, this is a systematic sample. This sampling method is not as representative of the entire population as a random sample, because each member of the population does not have an equally likely chance to be included, only the members that fit the pattern will be. Determine which sample method makes a specific sample more representative for a population.
 

Sample Problems

(1)

You need to find the most popular sport. Which sampling method would work best to help you?

A) Ask your friends. B) Ask the basketball team.

C) Ask random students off a list of all students. D) Ask the coach.

(C)

(2)

Tatem needed to find the favorite ice cream of boys in her class. She asked the every other boy as they walked into homeroom. What kind of sample did Tatem take?

(systematic)

(3)

Kelly wanted to find the favorite pop star of jr. high girls at her school. She walked around the cafeteria at lunch and asked each girl inside. What kind of sample did Kelly use?

(convenience)

(4)

Jacob was given the assignment to find the most popular summer movie for jr. high kids in Encino, California. He stood outside a movie theatre in Encino for 3 hours and asked the jr. high kids that were going in. What kind of survey did he conduct? Was it representive for the entire population?

(Since Jacob used a convenience sample, it was not representative of the entire population. Kids on the other side of town were left out.)

(5)

Gwen was asked to collect data to find the most popular video game amongst the students at her jr. high. The principal gave her a set of cards with the names and phone numbers for all students at the jr. high. Gwen placed the cards in a box and shook it up. She then drew out the cards one at a time, called the student and put the card back. She surveyed a total of 20 students out of the 432 in the box. What kind of sample did Gwen use? Would her survey likely be representative of the population?

(random. Yes, each student had an opportunity to be chosen, even though she only chose 20.)

Learning Tips

(1)

In order for a sample to be representative of a population, it must give each member of a group an opportunity to be a part of the sample. 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 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.

(2)

The most reliable sample is a random sample. Discuss the meaning of the word random with your child. Be sure that he or she understands that you can’t control random events. A random sample is called such because everyone in the population has the opportunity to be in the sample, but participants will be chosen at random with no rhyme or reason. Be sure to discuss common ways this is done: drawing sticks, pulling names out of a hat, even the lottery numbers drawn. You may want to have your child draw a poster listing or illustrating all the random samples he/she can think of. It is also important to note that when taking a random sample the item drawn out of the pool of names should always be placed back in. This needs to be done so that everyone has an equal opportunity. If the names, cards, sticks, etc… are not returned to the original pile, the next person drawn will have a better chance at being chosen.

(3)

The next type of sample is a systematic sample. Have your child think about the base word, system. Discuss how a systematic sample has a system built in to choose the sample. The system is a pattern. Though this pattern can change from survey to survey; all systematic surveys have one thing in common, they follow a pattern. An example of a systematic survey would be interviewing every 5th customer in a door, or calling every other person on the class list.

(4)

The last and easiest sample type is a convenience sample. Be sure that your child understands what convenience means. You can also discuss the base word, convenient or talk about what a convenience store is. You child should understand that the word convenience is related with the words quick and easy. Since a convenience sample is the quickest and easiest way to conduct as survey. However, it is often the least reliable representation of a group. An example of a convenience survey would be your child using his/her friends as a sample group or a teacher asking only his/her class about the favorite song of students at an entire school. This survey often excludes too many people to be considered representative of the population.

(5)

If you’d like to make these sampling ideas stick with your kinesthetic learner, have him/her try each kind of survey with the same population. He/she can come up with a survey question. Next, he/she will need to choose a population (i.e. kids on the block, neighbors, family members, etc…). After choosing the population discuss different ways he/she can conduct each survey type. Here are some suggestions:

Random: Put all population names in a hat and draw out five. Now go ask those 5.

Systematic: Write down the name and phone numbers or addresses of everyone in the population and then choose a pattern to follow. For example, call or visit every other person on the list.

Convenience: Find a place that will be easy to get find many people from the population and conduct your survey there. (i.e. neighborhood park).

Extra Help Problems

(1)

You need to find the most popular desert for kids in your after school program. There are total of 30 kids in the program. Which sampling method would work best to help you?

A) Ask your all the kids in the program.

B) Ask the first five kids that come in the door.

C) Ask the staff.

D) Ask random students off a list of all students.

(A)

(2)

You need to find the most popular desert for kids in your jr. high. There are total of 687 kids in your jr. high. Which sampling method would work best to help you best represent the entire student body?

A) convenience

B) systematic

C) random

D) population

(C)

(3)

You need to find the most popular radio station for teens in your city. Which sampling method would work best to help you best represent the majority of teens in your city?

A) Ask all your friends.

B) Send a set of 20 surveys to the five high schools in your area and have students randomly chosen fill them out and return them.

C) Stand outside the high school in your neighborhood and survey students as they leave for the day.

D) Send out a survey to all teens in the entire city and have them mail them to you.

(B)

(4)

You have 15 minutes and need to find the most popular subject area for 6th grade boys at your school. Which sampling method would work best to help you best represent the target population?

A) convenience

B) systematic

C) random

D) population

(A)

(5)

You have one day to find out the most popular movie for all students at your jr. high. Which sampling method would work best to help you best represent the entire student body?

A) Ask as many students as you can before school, after school and during breaks.

B) Ask every fifth student in each of your classes.

C) Ask your friends and your friends friends.

D) Ask the teachers.

(A)

(6)

Maddie needed to find the favorite car of boys in his class. She asked the every fourth boy on the class list. What kind of sample did Maddie use?

(systematic)

(7)

Mark wanted to find the favorite t.v. show for 6th graders at his school. He asked all the sixth graders he saw walking in the main in the morning?

(convenience)

(8)

Jayden was given the assignment to find the most popular summer beverage for teenagers in his town. He stood outside a convenience store in his town for 2 hours and asked the teenagers that were going in what there favorite summer drink was. What kind of survey did he conduct? Was it representative for the entire population?

(Since Jayden used a convenience sample. It was not representative of the entire population, because only the teens that went to that store on that day were asked.)

(9)

Natalia was asked to collect data to find the most popular summer movie amongst the students in summer school. The principal gave her a set of cards with the names and phone numbers for all students at the jr. high. Natalia placed the cards in a hat and mixed them up. She then drew out the cards one at a time, called the student and put the card back. She surveyed a total of 25 students out of the 102 in the box. What kind of sample did Gwen use? Would her survey likely be representative of the population?

(random. Yes, each student had an opportunity to be chosen, even though she only chose 25.)

(10)

A cereal company wanted to conduct a survey to find the most popular cereal amongst 4th graders in California. They had the 4th grade teachers at the owner’s son’s school collect data on the favorite cereal of their students. What kind of survey was conducted? Would this survey likely be representative of the population?

(Convenience. No, students from different cities and neighborhoods should be allowed to participate in the survey.)

 

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