11.15: Displaying by Type of Data
Have you ever conducted a survey?
After all of this research about the Iditarod, Thomas is inspired. He wants to conduct a survey of his classmates about the Iditarod.
First, Thomas has to decide upon a question. He wants to know how many \begin{align*}7^{th}\end{align*} graders would be willing to race in the Iditarod when they are 18 years old. He knows that a good survey question will use who, what, when, where or how. He decides to use this question.
“Would you be willing to race in the Iditarod in Alaska when you are 18 years old?”
After learning about the youngest person to ever race in the Iditarod, Thomas decided to make his question very specific for age. The youngest person to ever race in the Iditarod was Dallas Seavey in 2005. He was just 18 years old. He has raced it several times since.
Now that Thomas has his question, he needs to figure out which sample he is going to use. He wants to survey \begin{align*}7^{th}\end{align*} graders like himself. Thomas only wants to survey \begin{align*}7^{th}\end{align*} graders so that his sample will be accurate.
Thomas knows of two great places to survey students. He has narrowed it down to either the \begin{align*}7^{th}\end{align*} grade adventure program or the \begin{align*}7^{th}\end{align*} grade lunch in the cafeteria. His concern about the adventure program is that not all of the students are enrolled in it. With the cafeteria, every student in the \begin{align*}7^{th}\end{align*} grade attends lunch at the same time.
Thomas is puzzled. He begins to think carefully about which group is the best survey.
What do you think? Do you have an idea why one sample group might be better versus another? This Concept is all about surveys. You will learn all about them and why one sample creates a more accurate report. By the end of this Concept, you will know how to help Thomas with his dilemma.
Guidance
Surveys are used to collect information about a population or group of individuals. When a company would like to know if a group of people will purchase a new product, they create a survey. When a teacher would like to know if her students will participate in an after school science club, she creates a survey.
The first step in surveying a group of people is to write an unbiased question. Good survey questions are short and concise and usually begin with “Who, What, When, Where, Why, or How.”
The next step is to choose a random sample of participants. In a random sample, each member of a group has an equal chance at being asked to participate in the survey.
After the results of the survey are in, statisticians analyze the data and use it to make estimates about groups of people.
Then you can create a visual display of the data.
You have had lots of opportunities to graph data taken from surveys. In this lesson, you will learn to devise a survey question, to choose a random sample of participants, to choose an appropriate display for the survey results, and to analyze the data to make predictions about a group of individuals.
Write down the steps to conducting a survey in your notebook. There are four steps to the process.
Now let's look at a situation that involves a survey.
Twenty-five households were asked to participate in a survey in which they were asked to approximate the number of hours they watch T.V. each day. The results of the survey are listed on the table below. Determine the most appropriate display for the given data.
\begin{align*}4 \quad 7 \quad 2 \quad 1 \quad 0 \quad 5 \quad 3 \quad 4 \quad 5 \quad 2 \quad 1 \quad 0 \quad 3 \quad 4 \quad 5 \quad 6 \quad 3 \quad 2 \quad 1 \quad 2 \quad 3 \quad 6 \quad 4 \quad 5 \quad 4\end{align*}
A frequency table and histogram will depict the most and least frequent number of hours of television watched.
Interval (Hours of Television) | Tally | Frequency |
---|---|---|
0 – 1 | I I I I I | 5 |
2 – 3 | I I I I I I I I | 8 |
4 – 5 | I I I I I I I I I | 9 |
6 – 7 | I I I | 3 |
Now let’s draw some conclusions based on the data and the display.
Looking at the histogram, you can see that the majority of families that participated in the survey watch between four and five hours of television each night. Five families watch between zero and one hours of television each night. Eight families watch between two and three hours of television nightly. Three of the twenty-five families watch between six and seven hours of television each night.
One hundred people were asked to participate in a survey about cereal. Participants were asked to choose their favorite from a list of ten cereals. The results of the survey are listed below.
Cereal | Amount |
---|---|
Fruit Flakes | 12 |
Chocolate Puffs | 18 |
Oat-O’s | 9 |
Raisin Delight | 3 |
Honey Crunch | 17 |
Bran Loops | 3 |
Oat Squares | 9 |
Fiber Max | 2 |
Fruities | 10 |
Cinnamon Squares | 17 |
Display the results on a bar graph to compare the results for each type of cereal.
A population is a group about which you want information. Because it is impossible to survey an entire population, a sample or part of the population is chosen to participate in the survey. The results from the sample group are used to make estimates about the population. Larger samples lead to more reliable estimates about the population. In a random sample each member of the population has an equal chance of being chosen to participate in the survey. Using random samples reduce the likelihood of bias.
It is important to create and conduct a survey without bias.
The first way to prevent bias is to ensure that participants are chosen randomly. For example, if surveying high school students about their favorite sport, it would be bias to take your only sample at the Friday night football game. Your survey results will be valid and reliable if for example, you survey every fifth student that walks through the hallway.
A well written survey question is another way to prevent bias. Survey questions should be written clearly and concisely and should begin with “Who, What, When, Why, Where, or How.”
You would like to conduct a survey to determine what activities middle school students like to do on the weekends. To ensure an unbiased sample, you should:
a. Go to the mall and survey every tenth person that walks by.
b. Survey middle school students at a local movie theatre.
c. Survey every fifth person leaving each of your classes.
“C” is the best answer. You should avoid taking the survey at the mall and the movies because it is likely that those participants will all say the mall or the movies as their favorite activity.
Being aware of bias is the best way to ensure that your survey is accurate.
Here is the original problem once again. Reread it and then read the conclusion to the problem at the end.
After all of this research about the Iditarod, Thomas is inspired. He wants to conduct a survey of his classmates about the Iditarod.
First, Thomas has to decide upon a question. He wants to know how many \begin{align*}7^{th}\end{align*} graders would be willing to race in the Iditarod when they are 18 years old. He knows that a good survey question will use who, what, when, where or how. He decides to use this question.
“Would you be willing to race in the Iditarod in Alaska when you are 18 years old?”
After learning about the youngest person to ever race in the Iditarod, Thomas decided to make his question very specific for age. The youngest person to ever race in the Iditarod was Dallas Seavey in 2005. He was just 18 years old. He has raced it several times since.
Now that Thomas has his question, he needs to figure out which sample he is going to use. He wants to survey \begin{align*}7^{th}\end{align*} graders like himself. Thomas only wants to survey \begin{align*}7^{th}\end{align*} graders so that his sample will be accurate.
Thomas knows of two great places to survey students. He has narrowed it down to either the \begin{align*}7^{th}\end{align*} grade adventure program or the \begin{align*}7^{th}\end{align*} grade lunch in the cafeteria. His concern about the adventure program is that not all of the students are enrolled in it. With the cafeteria, every student in the \begin{align*}7^{th}\end{align*} grade attends lunch at the same time.
Thomas is puzzled. He begins to think carefully about which group is the best survey.
When Thomas began to think about the two groups, he started to develop some ideas why one might be a better survey group than the other. He started with the adventure group.
Adventure Group
-loves outdoor adventure
-probably has heard of the Iditarod
-enthusiastic about outdoor challenges
-not everyone is registered-not an accurate sample of all of the \begin{align*}7^{th}\end{align*} grade
Then Thomas began to think about his question. Because he wants to know how many \begin{align*}7^{th}\end{align*} graders would be willing to race in the Iditarod when they are 18 years old, he needs to sample the largest group of \begin{align*}7^{th}\end{align*} graders that he can.
Because every \begin{align*}7^{th}\end{align*} grader eats lunch at the same time in the cafeteria, asking every other person in line for lunch the question will give Thomas a lot of information for his survey.
Then he call tally his results and report his findings.
Vocabulary
Here are the vocabulary words in this Concept.
- Survey
- information gathered about people’s opinion on a particular topic or activity.
- Population
- a group of people
- Random Sample
- a sample where everyone in a group has an equal chance of answering the survey question.
- Sample
- the part of a population that participates in a survey.
Guided Practice
Here is one for you to try on your own.
Recall that twenty-five families were asked to state the number of hours they watch television each day. Use the results from the survey to answer the questions below.
Interval (Hours of Television) | Tally | Frequency |
---|---|---|
0 – 1 | I I I I I | 5 |
2 – 3 | I I I I I I I I | 8 |
4 – 5 | I I I I I I I I I | 9 |
6 – 7 | I I I | 3 |
Answer
What percentage of participants stated they watch between four and five hours of television per day?
Nine participants out of twenty-five stated that they watch between four and five hours of television per day. To determine the percentage, express nine out of twenty-five as a fraction. This can be converted to an equivalent fraction with a denominator of one hundred. To do so, multiply the numerator and denominator by four.
\begin{align*}& \underline{9} \times 4 = \underline{36} = 36 \% \\ & \frac{36}{100}\end{align*}
36% of the participants stated that they watch between four and five hours of television each day.
Video Review
Here is a video for review.
This is a Khan Academy video on surveys and samples.
Practice
Directions: Use the information provided to answer the following questions.
One hundred people were asked to participate in a survey about travel. Participants were asked to state whether they had visited each of the cities listed below.
City | Number of People Who Visited: |
---|---|
Waikiki | 85 |
New York City | 80 |
San Francisco | 87 |
Chicago | 54 |
Dallas | 35 |
Orlando | 38 |
Atlanta | 50 |
Seattle | 44 |
Denver | 32 |
1. Create a bar graph of the data.
2. What percent of the people visited Waikiki?
3. What percent of the people visited Denver?
4. What percent of the people did not visit Dallas?
5. What percent of the people did not visit Chicago?
6. Which city had more people visited than any other city?
7. Which city had less people visited than any other city?
Thirty students were selected at random at Montgomery High School. Each participant was asked to state the number of textbooks they were carrying at that moment. The results of the survey are depicted below. Choose the best display to depict the data. Then use the graph you created to answer the questions below.
\begin{align*}& 0 \qquad 2 \qquad 4 \qquad 3 \qquad 1\\ & 2 \qquad 5 \qquad 0 \qquad 4 \qquad 3\\ & 2 \qquad 5 \qquad 4 \qquad 3 \qquad 2\\ & 1 \qquad 0 \qquad 0 \qquad 2 \qquad 3\\ & 5 \qquad 6 \qquad 1 \qquad 2 \qquad 4\\ & 5 \qquad 6 \qquad 3 \qquad 2 \qquad 3\end{align*}
8. Which graph is the best display of the data?
9. Create that graph here.
10. What percent of the students had the most common amount of books in their backpack?
11. What percent of the students had between four and seven books in their backpack?
12. How many students had 1 book in their backpacks?
13. How many students had 0 books in their backpacks?
14. What percent had 1 book?
15. What percent had 0 books?
Create a survey question. Decide who will be the sample population. Write a few sentences to describe who will take part in the survey and how you will administer the survey. Administer the survey, record the results on a table. Choose the most appropriate display for the data. Use these questions for guidance.
16. What is your sample population?
17. How many people are in the sample?
18. Does your question use who, what, when, where or how?
19. Is your sample biased, why or why not?
20. Are your results what you expected?
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Population
In statistics, the population is the entire group of interest from which the sample is drawn.Random Sample
A random sample is a subset of a population for which each member of the population has an equal chance of being chosen.Sample
A sample is a specified part of a population, intended to represent the population as a whole.Survey
A survey is a method of collecting data where you ask a sample of people the same question.