6th Grade - Samples Of The Population

 
     
 
     
 
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6th
Statistics
Samples of the Population
Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.
Data is normally collected to answer a specific question. If data is being collected from the entire group, the population is being studied. A survey taken of the population will always be the most representative of the group. However, if the population is too large to study each part individually, a sample will be taken. A sample is a survey that is taken by only looking at part of a population. There are different types of samples that can be taken. If a sample is taken from a group that already exists (ex. 6th period math students or friends) it is called a convenience sample. 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.
 

Sample Problems

(1)

Mr. Lee asked Liliana to take a survey to find out the top 10 songs to request from the deejay at the end of the year dance. Liliana asks ten of her friends their favorite songs. She says that because they are all 6th graders they will represent the songs the 6th graders in her school like the best. What is wrong with Liliana’s statement?

(The sample is biased and not randomly chosen. It is biased because she only asked her friends, who probably like what she likes. Her survey is too small for the entire 6th grade and not likely to be representative of the entire grade level.)

(2)

Pedro’s math teacher asked him to conduct a survey of the favorite school lunch of the student body at his school, grades K-8. There are 824 students at his school. Should Pedro interview all the students at his school or take a sample?

(Pedro will need to take a sample. It will take him too long to survey all 824 students.)

(3)

Khoa’s computer teacher asked him to conduct a survey of how many computers the students in the class has in their home. There are 20 students in the class. Should Khoa survey all the students in the class or take a sample?

(Khoa should survey the entire population. A population survey always gives the most exact measure, while a sample just gives a good estimate. The population is small enough to complete the survey quickly and easily since all students are in the same class. So, there is no reason for Khoa to take a sample.)

(4)

You are asked to collect data on the most popular bands amongst 6th graders in California. What would be the best way to conduct this survey in order to best represent the population?

(I would need to randomly survey 6th graders from all over California.)

(5)

Identify the population in the survey. Stacy collected data from the teachers at her school to find what their favorite flavor of ice cream is.

(teachers at her school)

Learning Tips

(1)

It is important to understand the difference between the population and a sample. The population is the entire group. You may want to discuss with your child different populations in their lives (school, female, male, etc….). Next, discuss how a sample is only part of a group. An easy visual for this is to talk about when you are given a sample of a part of a food or drink at the grocery store. This will allow your child to visualize that a sample is just a small part of something larger. For the kinesthetic learner, you could even allow him/her to use food items around the house to cut a sample size portion. Be sure to discuss how the whole thing is the population and the part is the sample.

(2)

The visual child can draw pictures of populations vs. samples. He/she will begin by folding a paper in half and opening it again to create two columns. Next, he/she will draw pictures of different populations around the world; even animal populations will work. Just be sure that he/she understands that the population is the entire group (so there should be many figures in the drawings). After a few populations have been drawn, the artist will draw a sample of each population in the column to the right of the original population. So, if a child had drawn a population of say 20 giraffes, he/she would just draw 4 or 5 to represent the sample or if he/she drew the population of his/her class, the sample would be just a few of the students.

(3)

It is important that children understand how to find the population that is being represented in a survey or sample. Practice reading sample problems and be sure your child can tell you who the survey is targeting.

(4)

Be sure that your child is able to determine when to use a population and when it is appropriate to use a sample. Since a sample is less representative of the entire group, when at all possible, a population should be used. However, more often than not, a population is too large to collect data on. When a population is too large, it is appropriate to use a sample. The type of sample used will be important and should be considered carefully.

(5)

Be sure that your child understands the different types of samples. The sample names are new vocabulary for most children. 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. 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. The last 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, 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 only asking his/her class about the favorite song of students at an entire school.

Extra Help Problems

(1)

Ms. Kimora asked Jared to take a survey to find out the top 20 songs to request from the deejay at the end of the year dance. Jared asks 20 guys he plays soccer with their favorite songs. He says that because they are all 6th graders they will represent the songs the 6th graders at his school like the best. What is wrong with Jared’s statement?

(The sample is biased and not randomly chosen. It is biased because he only asked guys. His survey is too small for the entire 6th grade and not likely to be representative of the entire grade level, especially the girls.)

(2)

Amanda’s math teacher asked her to conduct a survey of the favorite sport of the student body at her jr. high. There are 635 students at her school. Should Amanda interview all the students at his school or take a sample?

(Amanda will need to take a sample. It will take her too long to survey all 635 students.)

(3)

Eric’s science teacher asked him to conduct a survey of how many pets each student in the class has in their home. There are 30 students in the class. Should Erik survey all the students in the class or take a sample?

(Erik should survey the entire population. A population survey always gives the most exact measure, while a sample just gives a good estimate. The population is small enough to complete the survey quickly and easily since all students are in the same class. So, there is no reason for Eric to take a sample.)

(4)

You are asked to collect data on the most popular bands amongst 6th graders in California. What would be the best way to conduct this survey in order to best represent the population?

(I would need to randomly survey 6th graders from all over California.)

(5)

Identify the population in the survey. Willie collected data from 25 third graders at his school to find what their favorite sport.

(3rd graders at his school)

(6)

Joe needed to collect data on the average hours 8-12 boys watch t.v. in Huntington Beach. He sent surveys to 35 schools in California and asked each principle to randomly choose one student to complete the survey. Who was Joes target population?

(8-12 year old boys living in California)

(7)

Lacey’s soccer coach asked her to survey the team to find out a favorite color for a new uniform. Lacey asked the five best players on the team. Who was supposed to be the target population? Was Lacey’s survey method representative of the entire team?

(Lacey’s soccer team. No, her sampling method was not representative of the entire team. She only gave the star players a chance to be surveyed when all players should have been given equal opportunity. Lacey should’ve done a population survey._

(8)

Timmy decided to collect data to determine the most popular car amongst teenage boys at Jackson High. He received a list of names and phone numbers for all boys ranging in age from 15-19 at the high school. He then called every 15th boy on the list to complete the survey. Who was Timmy’s target population? Was his survey method representative of this population.

(teenage boys at Jackson High. His sampling method was fairly representative of the population, because he used a list of all teenage boys at the high school and conducted a systematic sample. However, a random sample would have been even more representative.)

(9)

You are asked to collect data on the most popular videogame amongst 6th graders at three jr. high school in your area. What would be the best way to conduct this survey in order to best represent the population?

(Conduct a random survey at all three schools.)

(10)

You are asked to collect data on the most popular bands amongst 6th girls in your school. There are 43 girls in the 6th grade. What would be the best way to conduct this survey in order to best represent the population?

(Conduct a population survey. This can be done quickly and easily, by having each homeroom teacher deliver and collect the surveys from the girls.)


(11)

Determine whether a population or sample survey should be taken.

Donna needs to find out the most popular ice cream flavor for the kids attending her 12th birthday party.

(population)

(12)

Jason needs to determine the most popular basketball shoe for NBA players.

(sample)

(13)

Holly would like to find the name of the most popular fashion designer amongst teenage girls in New York.

(sample)

(14)

Shane wants to find the number of hours spent on Science homework for the students in his Biology class.

(population)

(15)

Mandie needs to collect data to find the favorite book of 6th graders in Los Angles County.

(sample)

 

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