# 6th Grade - Sampling Errors And Bias

 Grade Level: 6th Skill: Statistics Topic: Sampling Errors and Bias Goal: Identify data that represent sampling errors and explain why the sample (and the display) might be biased. Skill Description: Study data displays (i.e. graphs, charts, tables, etc…) and sample type used to compile a set of data. Determine if the data display and/or data conclusion have been influenced by the sample type (convenience, random or systematic). There are three main sample types and each represents a population very differently. 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. Another word for biased is prejudiced. 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. 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.

## 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. Why might the sample give misleading results?

(The survey only asked young people, some of which, not even being licensed drivers.)

(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. Why might this sample give misleading results?

(The survey does not specify women’s shoes. Since only the women are being surveyed, this leave the men under-represented.)

(3)

Tasha was asked to conduct a survey to find the favorite pizza topping in her class. She asked the 5 students that sit at her table. Is her sample representative of the entire class? Explain.

(The sample is biased, because Tasha didn’t give everyone a fair chance to share his/her favorite topping.)

(4)

Star Video wanted to find the most popular movie type. They surveyed every 5th person that walked in to rent a movie on Tuesday. Is their sample representative of their clientele? Explain.

(This sample is biased, because it only includes the every 5th video member that happened to come into the store on Tuesday.)

(5)

A group of people were given a survey about senior citizen discounts. The table below shows the percentages of people surveyed in different age groups. Why might the sample be biased?

 Ages teens 20s-30s 40s-50s 50s-60s 70 & up Percent 18% 35% 35% 8% 4%

(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.)

### Online Resources

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### Extra Help Problems

(1)

A group of people were surveyed about their favorite presidential candidate. The results showed that 85% of the population was voting for the Democratic candidate. The sample group included teenagers ranging in age from 14-19. Why might the sample give misleading results?

(The survey only asked young people, many of which are not even old enough to vote.)

(2)

A survey was conducted by a department store to find the most clothing designer for 11-15 year old girls. The store sent surveys to the parents of girls that shopped in the store in December. Why might this sample give misleading results?

(The survey was filled out by parents, yet they are seeking the opinion of the young girls.)

(3)

Tiffany was asked to conduct a survey to find the most favored ice cream in her Karate class. She asked all the girls when she walked in. Is her sample representative of the entire class? Explain.

(The sample is biased, because Tiffany only asked the girls. The boys were under represented.)

(4)

Star Video wanted to find the most popular video game. They pulled out their members phone list and called every 25th person on it, until they had called 20 people. The last person they called was 35 years old. Is their sample representative of their clientele? The list is organized by age from 99 down to 16. Explain.

(This sample is biased, because it did not include the opinions of the younger members.)

(5)

A group of people were given a survey about a healthy diet. The table below shows the percentages of people surveyed in different age groups. Why might the sample be biased?

 Ages teens 20s-30s 40s-50s 50s-60s 70 & up Percent 60% 10% 10% 10% 10%

(This sample and display is biased because most of the sample is made up of teens. The other age groups are not evenly represented.)

(6)

A radio station wants to survey its listeners to determine the favorite bumper sticker style. It hosts a remote broadcast at Sycamore High School and interviews all kids that stop by the broadcasting tent. Why might the survey be biased?

(This sample is biased because it only includes high school students.)

(7)

A car dealership wants to survey its customers to determine the favorite car color. They email the customer that bought cars in the last four weeks. Why might the sample be biased?
(This sample is biased because only recent car purchasers have the opportunity to participate.)

(8)

A local baby formula company wants to survey new moms to find out what kind of formula their baby drinks. They go to a local hospital and survey all the moms that just had babies. Why might the sample be biased?

(This convenience sample is biased. They only have results from one hospital in the area and just a handful of the new moms.)

(9)

You need to conduct a survey of the most popular basketball shoe amongst middle school students. You ask your school’s basketball team. Why might your sample be biased?

(This sample is biased, because a huge majority of the middle school have been left out of the survey.)

(10)

Your best friend needed to conduct a survey to determine the favorite subject of 5th grade boys and girls. She surveyed 35 girls and 8 boys. Why might her survey be biased?

(The sample is biased against the boys, because she asked the opinions of 35 girls and only 8 boys.)