Identify data that represent sampling errors and explain why the sample (and the display) might be biased.

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.

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 5^{th} 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 5^{th} 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.)

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. 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 5^{th} graders and you only ask girls, the boys are not being represented. Thus, you would need to include 5^{th} 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.

(2)

The most reliable sample is a random sample. It is important you’re your child is able to identify this type of sample. 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. 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. If your child is able to identify a survey type as a random sample where all people or objects in the target population had equal opportunity to be interviewed, then the sample is most likely unbiased. The exception to this is if by chance all the names/items drawn just happened to represent just one part of a sample group. For instance, if a teacher placed all the names of all students in a basket and then drew out 10 and all 7 happened to be boys and 2 girls, the sample would be biased because boys and girls weren’t evenly represented.

(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 5^{th} customer in a door, or calling every other person on the class list. When looking for biased systematic samples, watch for the survey set up. For example, if every fifth customer that comes in the door on Friday is interviewed it as not as representative as a survey conducted for every fifth customer in the door everyday for a given week.

(4)

The last and easiest sample type is a convenience sample. 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)

Always be on the lookout for sampling errors. Sampling errors can cause misleading data displays and incorrect data conclusions. Knowing the wide spectrum of kinds of people or objects in a target population will help. When in doubt, write down notes. Then try to match your notes to that data display. If a part of the population from your notes is not included in the data display, you know that the conclusion is biased. Be sure that you can explain what is wrong with a sample. Practice this with your child by giving a sample scenario. (i.e. John wanted to find the favorite color of the guys on his soccer team. He asked the 5 starters). Begin by looking at the population: soccer team, whole team. Next, discuss whom he actually used as the sample (just the 5 starters). Think about who was left out (all the second string players). Discuss why John’s survey would be biased against the second string players.

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 25^{th} 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 5^{th} 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.)