What if you polled the students in your class and asked them who their favorite math teacher is in your school? How could you graphically display the results? After completing this Concept, you'll be able conduct a survey like this, display your results in a pie or bar chart, and analyze and interpret the results.
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CK12 Foundation: Designing, Conducting and Analyzing Surveys
Guidance
A survey is a way to ask a lot of people a few wellconstructed questions. The survey is a series of unbiased questions that the subject must answer. Some advantages of surveys are that they are efficient ways of collecting information from a large number of people, they are relatively easy to administer, a wide variety of information can be collected and they can be focused (researchers can stick to just the questions that interest them.) Some disadvantages of surveys arise from the fact that they depend on the subjects’ motivation, honesty, memory and ability to respond. Moreover, answer choices to survey questions could lead to vague data. For example, the choice “moderately agree” may mean different things to different people or to whoever ends up interpreting the data.
Conducting a Survey
There are various methods for administering a survey. It can be done as a faceto face interview or a phone interview where the researcher is questioning the subject. A different option is to have a selfadministered survey where the subject can complete a survey on paper and mail it back, or complete the survey online. There are advantages and disadvantages to each of these methods.
The advantages of facetoface interviews include fewer misunderstood questions, fewer incomplete responses, higher response rates, and greater control over the environment in which the survey is administered; also, the researcher can collect additional information if any of the respondents’ answers need clarifying. The disadvantages of facetoface interviews are that they can be expensive and timeconsuming and may require a large staff of trained interviewers. In addition, the response can be biased by the appearance or attitude of the interviewer.
The advantages of selfadministered surveys are that they are less expensive than interviews, do not require a large staff of experienced interviewers and can be administered in large numbers. In addition, anonymity and privacy encourage more candid and honest responses, and there is less pressure on respondents. The disadvantages of selfadministered surveys are that responders are more likely to stop participating midway through the survey and respondents cannot ask them to clarify their answers. In addition, there are lower response rates than in personal interviews, and often the respondents who bother to return surveys represent extremes of the population – those people who care about the issue strongly, whichever way their opinion leans.
Designing a Survey
Surveys can take different forms. They can be used to ask only one question or they can ask a series of questions. We can use surveys to test out people’s opinions or to test a hypothesis.
When designing a survey, the following steps are useful:
 Determine the goal of your survey: What question do you want to answer?
 Identify the sample population: Whom will you interview?
 Choose an interviewing method: facetoface interview, phone interview, selfadministered paper survey, or internet survey.
 Decide what questions you will ask in what order, and how to phrase them. (This is important if there is more than one piece of information you are looking for.)
 Conduct the interview and collect the information.
 Analyze the results by making graphs and drawing conclusions.
Example A
Martha wants to construct a survey that shows which sports students at her school like to play the most.
a) List the goal of the survey.
b) What population sample should she interview?
c) How should she administer the survey?
d) Create a data collection sheet that she can use to record her results.
Solution
a) The goal of the survey is to find the answer to the question: “Which sports do students at Martha’s school like to play the most?”
b) A sample of the population would include a random sample of the student population in Martha’s school. A good strategy would be to randomly select students (using dice or a random number generator) as they walk into an allschool assembly.
c) Facetoface interviews are a good choice in this case. Interviews will be easy to conduct since the survey consists of only one question which can be quickly answered and recorded, and asking the question face to face will help eliminate nonresponse bias.
d) In order to collect the data to this simple survey Martha can design a data collection sheet such as the one below:
Sport  Tally 

baseball  
basketball  
football  
soccer  
volleyball  
swimming 
This is a good, simple data collection sheet because:
 Plenty of space is left for the tally marks.
 Only one question is being asked.
 Many possibilities are included, but space is left at the bottom in case students give answers that Martha didn’t think of.
 The answer from each interviewee can be quickly collected and then the data collector can move on to the next person.
Once the data has been collected, suitable graphs can be made to display the results.
Example B
Raoul wants to construct a survey that shows how many hours per week the average student at his school works.
a) List the goal of the survey.
b) What population sample will he interview?
c) How would he administer the survey?
d) Create a data collection sheet that Raoul can use to record his results.
Solution
a) The goal of the survey is to find the answer to the question “How many hours per week do you work?”
b) Raoul suspects that older students might work more hours per week than younger students. He decides that a stratified sample of the student population would be appropriate in this case. The strata are grade levels through . He would need to find out what proportion of the students in his school are in each grade level, and then include the same proportions in his sample.
c) Facetoface interviews are a good choice in this case since the survey consists of two short questions which can be quickly answered and recorded.
d) In order to collect the data for this survey Raoul designed the data collection sheet shown below:
Grade Level  Number of Hours Worked  Total number of students 

grade  
grade  
grade  
grade 
This data collection sheet allows Raoul to write down the actual numbers of hours worked per week by students as opposed to just collecting tally marks for several categories.
Display, Analyze, and Interpret Statistical Survey Data
In the previous section we considered two examples of surveys you might conduct in your school. The first one was designed to find the sport that students like to play the most. The second survey was designed to find out how many hours per week students worked.
For the first survey, students’ choices fit neatly into separate categories. Appropriate ways to display the data might be a pie chart or a bar graph. Let’s revisit this example.
Example C
In Example A Martha interviewed 112 students and obtained the following results.
Sport  Tally  

baseball  31  
basketball  17  
football  14  
soccer  28  
volleyball  9  
swimming  8  
gymnastics  3  
fencing  2  
Total: 112 
a) Make a bar graph of the results showing the percentage of students in each category.
b) Make a pie chart of the collected information, showing the percentage of students in each category.
Solution
a) To make a bar graph, we list the sport categories on the axis and let the percentage of students be represented by the axis.
To find the percentage of students in each category, we divide the number of students in each category by the total number of students surveyed:
Sport  Percentage 

baseball  
basketball  
football  
soccer  
volleyball  
swimming  
gymnastic  
fencing 
Now we can make a graph where the height of each bar represents the percentage of students in each category:
b. To make a pie chart, we find the percentage of the students in each category by dividing the number of students in each category as in part a. The central angle of each slice of the pie is found by multiplying the percentage of students in each category by 360 degrees (the total number of degrees in a circle). To draw a piechart by hand, you can use a protractor to measure the central angles that you find for each category.
Sport  Percentage  Central angle 

baseball  
basketball  
football  
soccer  
volleyball  
swimming  
gymnastics  
fencing 
Here is the piechart that represents the percentage of students in each category:
For the second survey, actual numerical data can be collected from each student. In this case we can display the data using a stemandleaf plot, a frequency table, a histogram, or a boxandwhisker plot.
Watch this video for help with the Examples above.
CK12 Foundation: Designing, Conducting and Analyzing Surveys
Vocabulary
 A stemandleaf plot consists of a vertical “stem” containing the first digit of each number, with the rest of each number written to the right of the stem like a “leaf.”
 A frequency table is one that records the frequency of each value in a data set.
 When the data we are representing falls into well defined categories (such as the integers 1, 2, 3, 4, 5 & 6) it is more appropriate to use a histogram to display that data. A histogram is a graph of a frequency table, where the frequency of each value is represented by the height of a bar.
 A boxandwhisker plot is formed by placing vertical lines at five positions, corresponding to the smallest value, the first quartile, the median, the third quartile and the greatest value. (These five numbers are often referred to as the five number summary .) A box is drawn between the position of the first and third quartiles, and horizontal line segments (the whiskers ) connect the box with the two extreme values.
 A pie chart is a circular graph where the proportion of data in each category is represented by an equivalent proportion of the circle.
Guided Practice
In Example B Raoul found that that 30% of the students at his school are in grade, 26% of the students are in the grade, 24% of the students are in grade and 20% of the students are in the grade. He surveyed a total of 60 students using these proportions as a guide for the number of students he interviewed from each grade. Raoul recorded the following data:
Grade Level  Number of hours worked  Total number of students 

grade 
0, 5, 4, 0, 0, 10, 5, 6, 0, 0, 2, 4, 0, 8, 0, 5, 7, 0 
18 
grade 
6, 10, 12, 0, 10, 15, 0, 0, 8, 5, 0, 7, 10, 12, 0, 0 
16 
grade 
0, 12, 15, 18, 10, 0, 0, 20, 8, 15, 10, 15, 0, 5 
14 
grade 
22, 15, 12, 15, 10, 0, 18, 20, 10, 0, 12, 16 
12 
a) Construct a stemandleaf plot of the collected data.
b) Construct a frequency table with bin size of 5.
c) Draw a histogram of the data.
d) Find the five number summary of the data and draw a boxandwhisker plot.
Solution
a) The ordered stemandleaf plot looks as follows:
We can easily see from the stemandleaf plot that the mode of the data is 0. This makes sense because many students do not work in high school.
b) We construct the frequency table by counting how many students fit in each category.
Hours worked  Frequency 

23  
12  
13  
9  
3 
c) The histogram associated with this frequency table is shown below.
d) The five number summary is as follows:
smallest number = 0
largest number = 22
Since there are 60 data points, . The median is the mean of the and the values:
median = 6.5
Since each half of the list has 30 values in it, then the first and third quartiles are the medians of each of the smaller lists. The first quartile is the mean of the and values:
first quartile = 0
The third quartile is the mean of the and values:
third quartile = 12
The associated boxandwhisker plot is shown below.
Practice
 Make a pie chart for the problem in the Guided Practice.
 Melissa conducted a survey to answer the question “What sport do high school students like to watch on TV the most?” She collected the following information on her data collection sheet.
Sport  Tally  

baseball  32  
basketball  28  
football  24  
soccer  18  
gymnastics  19  
figure skating  8  
hockey  18  
Total:  147 
a) Make a piechart of the results showing the percentage of people in each category.
b) Make a bargraph of the results.
 Samuel conducted a survey to answer the following question: “What is the favorite kind of pie of the people living in my town?” By standing in front of his grocery store, he collected the following information on his data collection sheet:
Type of pie  Tally  

apple  37  
pumpkin  13  
lemon meringue  7  
chocolate mousse  23  
cherry  4  
chicken pot pie  31  
other  7  
Total:  122 
a) Make a pie chart of the results showing the percentage of people in each category.
b) Make a bar graph of the results.
 Myra conducted a survey of people at her school to see “In which month does a person’s birthday fall?” She collected the following information in her data collection sheet:
Month  Tally  

January  16  
February  13  
March  12  
April  11  
May  13  
June  12  
July  9  
August  7  
September  9  
October  8  
November  13  
December  13  
Total:  136 
a) Make a pie chart of the results showing the percentage of people whose birthday falls in each month.
b) Make a bar graph of the results.
 NamLing conducted a survey that answers the question “Which student would you vote for in your school’s elections?” She collected the following information:
Candidate  graders  graders  graders  graders  Total 

Susan Cho  19  
Margarita Martinez  31  
Steve Coogan  16  
Solomon Duning  26  
Juan Rios  28  
Total  36  30  30  24  120 
a) Make a pie chart of the results showing the percentage of people planning to vote for each candidate.
b) Make a bar graph of the results.
 Graham conducted a survey to find how many hours of TV teenagers watch each week in the United States. He collaborated with three friends that lived in different parts of the US and found the following information:
Part of the country  Number of hours of TV watched per week  Total number of teens 

West Coast  10, 12, 8, 20, 6, 0, 15, 18, 12, 22, 9, 5, 16, 12, 10, 18, 10, 20, 24, 8  20 
Mid West  20, 12, 24, 10, 8, 26, 34, 15, 18, 6, 22, 16, 10, 20, 15, 25, 32, 12, 18, 22  20 
New England  16, 9, 12, 0, 6, 10, 15, 24, 20, 30, 15, 10, 12, 8, 28, 32, 24, 12, 10, 10  20 
South  24, 22, 12, 32, 30, 20, 25, 15, 10, 14, 10, 12, 24, 28, 32, 38, 20, 25, 15, 12  20 
a) Make a stemandleaf plot of the data.
b) Decide on an appropriate bin size and construct a frequency table.
c) Make a histogram of the results.
d) Find the fivenumber summary of the data and construct a boxandwhisker plot.
In exercises 710, consider the following survey questions.

“What do students in your highschool like to spend their money on?”
 Which categories would you include on your data collection sheet?
 Design the data collection sheet that can be used to collect this information.
 Conduct the survey. This activity is best done as a group with each person contributing at least 20 results.
 Make a pie chart of the results showing the percentage of people in each category.
 Make a bar graph of the results.

“What is the height of students in your class?”
 Design the data collection sheet that can be used to collect this information.
 Conduct the survey. This activity is best done as a group with each person contributing at least 20 results.
 Make a stemandleaf plot of the data.
 Decide on an appropriate bin size and construct a frequency table.
 Make a histogram of the results.
 Find the fivenumber summary of the data and construct a boxandwhisker plot.

“How much allowance money do students in your school get per week?”
 Design the data collection sheet that can be used to collect this information,
 Conduct the survey. This activity is best done as a group with each person contributing at least 20 results.
 Make a stemandleaf plot of the data.
 Decide on an appropriate bin size and construct a frequency table.
 Make a histogram of the results.
 Find the fivenumber summary of the data and construct a boxandwhisker plot.

“What time do students in your school get up in the morning during the school week?”
 Design the data collection sheet that can be used to collect this information.
 Conduct the survey. This activity is best done as a group with each person contributing at least 20 results.
 Make a stemandleaf plot of the data.
 Decide on an appropriate bin size and construct a frequency table.
 Make a histogram of the results.
 Find the fivenumber summary of the data and construct a boxandwhisker plot.