A group of boys decided to practice their times for the 400 meters one day after school. Five of the boys on the track team gathered together and all decided to practice. They figured out that the best way to do it was to have each person start in turns. One person would run, then the next and then the next until everyone had run. Carla came too so that she could run the stop watch and record the times.

All of the boys ran and at the end of it they asked Carla for the times. Although five boys ran, she had only recorded the scores of three boys.

“Why did you do that?” Marco asked.

“I only recorded the first three to cross the finish line,” Carla explained. “At the race, those will be the three winners.”

“But that isn’t accurate!” Marco explained.

Who is correct?

In this concept, you will learn to understand survey data.

### Surveys

A common tool that people use to gather information is a **survey**. A **survey** is a method of gathering information by collecting data on a sample of a larger **population**. A **population** can refer to any group about which information is desired. In other words, if you want to know about the opinions of students in your school, then the population is the entire school. The population could be an entire city, country, or even a group of plants, animals, or things.

As you can imagine, a population can be very large. For this reason, it is oftentimes impractical or even impossible to get information on every single member of the population. In order to save time and resources, you may survey only a small percentage of the population. In order to make sure that the information you gather from a smaller percentage is representative of the entire population, you use techniques to choose the members that you survey. When surveys are carried out appropriately, the information that they tell you can be very useful.

Let’s think about the different types of samples that can be collected.

**Random Sampling**

Monica can take a random sample by giving each student in the school an equal opportunity of being chosen. Like a lottery machine that uses ping pong balls to choose winning numbers, Monica would have to select students completely randomly. For example, if she had a list of students, she could mix up the names and choose the first 50 with her eyes closed.

**Stratified Random**

In this method, Monica would make sure that she selected an equal number of students from certain strata. **Strata** are different layers or levels. In her school, students are in levels by grade. In this case, strata can also refer to gender and educational program. If she randomly chooses 25 girls and 25 boys, she is using a stratified random method.

**Systematic Sampling**

Monica may also decide to sample students in a systematic manner. That is, she could stand at the front of the school or in the lunch line and sample every 20* ^{th}* student. This way, she would get approximately 50 students, assuming that they all attend school on the given day and they all come through the same door or go to lunch. If they do not, then she may not get a representative sample; the sample would be biased.

**Convenience Sampling**

If Monica finds these methods too difficult, she could go with an easier route and ask the first 50 students that walk by her homeroom, for example. This is called convenience sampling; it is the method that is easiest because it selects the members of the population to whom the sampler has the most access. The problem is that this method does not ensure a representative portion of the entire population. If she is in advanced biology, for example, and asks only students in that room or only students who walk by that room, they may have different views than students in the rest of the school. Perhaps the fact that they share a class or grade level with her will make them more likely to vote for her. That may not be true of the rest of the school.

**Self-Selected**

There are many people who like to be asked. They like that their opinion counts, they like to express their points-of-view, they like to participate, they like to help, or they like to influence an outcome. If Monica walks around with a sign that says, “Tell me how you feel about homework,” she allows members of the population to select themselves. You may have seen taste-tests in local malls, for example, that have signs reading: “Choose your favorite soda.” People who participate are self-selecting. As with convenience sampling, this may not be a representative portion of the population. People who do not select to participate may have different views from those that do participate.

Let’s look at an example.

There are 2000 students in Monica’s school. She wants to do a survey about student’s opinion on the new homework policy. She knows that she cannot ask everyone. She’ll have to take a sample, a small part of the population, and assume that the information they give her is true for the rest of the school. She plans to ask 50 people. In order to choose the 50 people that she asks, she can use a variety of methods.

When a survey is complete, there is still a lot of work to do. After collecting the data, it must be analyzed using a great many choices of displays and statistical measures. From these data analyses, you hope to make some generalizations about the population at large. You also hope, at times, to make decisions based on the data.

### Examples

#### Example 1

Earlier, you were given a problem about Carla running the stop watch and recording the times. She only recorded the first three to cross the finish line of the 400 meter race. Marco said she was not accurate as the runners all started at different times.

Marco is right. The boys all started at a different time. Therefore, the order that they crossed the finish line does not help in determining who was fastest. You have to calculate each time to figure this out. Time, not order, is what makes the difference here.

#### Example 2

A number of children were surveyed about the amount of time that they watch TV and the amount of time that they spend studying. The study was completed at a charter school that specializes in college preparation for first- generation Americans. Three students from each class were randomly chosen to participate in the survey. Their results are shown in the table below:

TV |
3.5 | 3.5 | 3.5 | 5 | 3 | 1 | 1 | 0 | 0 |

Studying |
2 | 1.5 | 2.5 | 1 | 3.5 | 4.5 | 5 | 5 | 1 |

TV |
1 | 2 | 2 | 2 | 1.5 | 0 | 0.5 | 4 | 4 |

Studying |
3.5 | 7 | 6 | 5.5 | 5 | 6 | 4 | 0.5 | 1 |

TV |
4 | 6 | 3 | 4 | 3 | 6 | 6.5 | 1 | 1 |

Studying |
1.5 | 1 | 4 | 2 | 4.5 | 0 | 0.5 | 7 | 1 |

The following conclusions were made.

- Montoya Charter School students who watch more than 2 hours of TV do not study.
- Children in the United States watch too much TV.
- Students who do not study enough will get low grades.
- TV is causing students to be less interested in school.

Draw a scatterplot to visually display this data. Analyze the conclusions that were made.

First, draw the scatterplot. Clearly, this data is difficult to interpret in this form. Because the school is looking for a relationship between TV time and studying time, a scatterplot is an excellent display of the data.

Next, analyze the conclusions that were made.

1. Montoya Charter School students who watch more than 2 hours of TV do not study.

The data shows that many students who watch more than 2 hours of TV do study although generally fewer hours.

2. Children in the United States watch too much TV.

This sample was only taken at a charter school that serves a specific population. You cannot generalize this data to other populations, like the entire United States.

3. Students who do not study enough will get low grades.

There is no data in this study that relates studying time to grades.

4. TV is causing students to be less interested in school.

A scatterplot does not imply causation, only correlation; the variables are shown to have a negative relation- ship, but that does not mean that one causes the other. If you take television time away from students, it does not mean that they will necessarily study more nor be more interested in school.

#### Example 3

Five students were surveyed in each of the seventh grade homerooms. What type of sampling method is this?

The answer is a stratified random sample.

#### Example 4

At a concert, the twentieth person in each of eight lines was asked about how he/she purchased his/her ticket. What type of sampling method is this?

The answer is a systematic sampling method.

#### Example 5

At a football game, only the people who agreed to be surveyed were surveyed. What type of sampling method is this?

The answer is a self- selected sampling method.

### Review

Define each of the following terms.

1. Survey

2. Random sample

3. Stratified sample

4. Systematic sample

5. Convenience sample

6. Self-Selected sample

Name each sampling method described below.

7. A mother asks everyone in her office-building about the best restaurant in town.

8. A police traffic stop pulls over every 3rd car to check for proper insurance.

9. A phone company uses a computer to choose customer for a satisfaction survey. 5% of each region are chosen randomly.

10. People call a phone number given on a receipt at a restaurant to answer questions about cleanliness and service. Each person who calls gets entered into a drawing.

11. A cattle herder checks for Mad Cow Disease by drawing blood from 30 cows that he chose by drawing their ID numbers from a hat.

12. Every fifth person to buy gasoline is asked about their automobile.

13. An announcement for a survey is mentioned at a movie theater. Anyone who chooses to participate can.

14. Every fifth grader at Smith School is asked about the number of hours he/she watches television per week.

15. A computer calls people from the phone book and asks them about their political choices.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 10.12.