SS - Analyzing Data Lesson

Analyzing Data Lesson

Let's collect some data!  You can answer these questions yourself or poll a friend or family member.

  1. What year were you born?
  2. What is your gender?
  3. How many text messages did you send yesterday?
  4. What does your cell plan charge for texting?
  5. How many people under the age of 18 live in your house?
  6. Which is your favorite food from the following choices: pizza, hamburgers, sushi, salad, chicken, other?
  7. Do you have a job that pays by the hour?
  8. If yes, how many hours do you work in an average week? (If no, put 0.)
  9. List how many hours you work a week (again) and then the average number of hours that you study a week.
  10. List your gender (again) and your shoe size.
  11. List your gender (again) and number of text messages (again).
  12. What is your favorite kind of music?

What do you think categorical data means? Data that can be summarized by counting the number of cases in each category. For example, gender, hair color, type of college or type of job, From the previous questions- year- gender yes/no, and kind of music are examples categorical data.

What do you think quantitative means? Numerical data that can be measured and summarized. For example, pulse, rate, speed, height, or cost. From the previous questions, year, cell phone charges, the number of people, the number of hours, shoe size and the number of text messages are example of quantitative date.  

What do you think univariate means?  Relates one piece of information or variable to each participant. Most of the questions above collects univariate data. 

What do you think bivariate means? Relates two piece of information or variables to each participant listing your gender shoe size or number of texts are bivariate. 

For categorical variables, we count up piles to display the distribution as a frequency table, bar chart or pie graph.

For quantitative variables, we slice up all the possible values into equal width bins. The bins give the distribution and are the building blocks for histograms. A histogram plots the bin counts as the heights of bars.

Using the data you collected in the poll, consider the these terms and how they relate to each question.  Then read below about about different graphical displays for data and consider which ones might be best for the data you collected in the poll.

Self Assessment

Survey 

survey that asks a response to the statements: School Uniforms should not be required (with Agree or Disagree) and Standardized dress can promote a productive school environment (with Agree or Disagree).

These questions show that the design of a survey can influence the results. Questions should be designed to be neutral and to allow the accurate recording of the opinions or facts given by the participants. For example, the uniform question could be worded as follows:

 

I am in favor of school uniforms for high school students.

 

Strongly agree        Agree   No opinion         Disagree     Strongly disagree

 

This is an example of a closed question because the participants are limited to the response choices that are given.

Closed questions are easier (and usually cheaper) to analyze, and sometimes a computer does much of the work. Open questions allow the participants to give more detailed responses. This approach, however, requires a follow-up analysis that is more labor intensive (and more expensive).

Reword the above question about school uniforms to make it an open question.

EXAMPLE: Describe your opinions about school uniforms for high school students.

When designing a survey (or an observation instrument), the researcher must also consider how the data will be collected. The following are some options:

  1. A face-to-face interviewer asks questions and records the answers of the participants (on paper or an electronic recording).
  2. A telephone interviewer asks questions and records the answers.
  3. A computer calls homes and records answers through key presses.
  4. A researcher observes behaviors or characteristics and marks the survey.
  5. A researcher hand-delivers surveys to participants, who then fill out the surveys and turn them back in.
  6. The survey is mailed to participants.
  7. The survey is e-mailed to participants.

Always bear in mind that whatever method of data collection is used, it is vitally important that the results be accurately interpreted and reported. This includes thoroughly disclosing the methods to the reader.

Histograms

Download Icon Indicator

Complete the Student Activity Sheets #5-16 to analyze histogram. Links to an external site.

Note: When you describe a distribution, you should always tell about its shape, center and spread.

Histograms Information

  • The center of the distribution is determined by the median or the middle value that divides the data values into two equal areas.
  • The spread of a distribution can be described by finding the range or the interquartile range.
  • Histograms may provide a well-defined summary of the distribution of a quantitative variable, but they don't show the values themselves.
  • Take a look at other graphical displays. Consider the characteristics of the center, shape, spread, and any unusual features

Boxplots and Dotplots

Download Icon Indicator

Complete the Student Activity Sheets #1-15 to examine other graphical displays. Links to an external site.

Bar and Pie Charts

1Example 1;

By the end of 2011, Facebook had over 146 million users in the United States. The table shows three age groups, the number of users in each age group, and the proportion (%) of users in each age group. Construct a bar graph and a pie chart using this data.

Data for Bar Graph
Age Groups Number of Facebook Users  Proportion (%) of Facebook Users
13-25 65,082,280 45%
26-44 53,300,200 36%
45-64 27,885,100 19%

 

Sample Bar Graph Sample Pie Chart

You try: 

1The population in Park City is made up of children, working-age adults, and retirees. The table shows the three age groups, the number of people in the town from each age group, and the proportion (%) of people in each age group. Construct a bar graph and a pie chart showing the proportions. Then check your answers below.

Data for Bar Graph
Age Groups Number of People  Proportion (%) of Population
Children 67,059 19%
Working-Age Adults 152,198 43%
Retirees 131,662 38%

 

Bar Graph with the data from the table      Pie Chart with the data from the table

 

For more practice creating and using Graphical Displays, go to Lumen Learning Links to an external site. and read about Histograms, Bar Graphs, Pie Charts, and Box Plots.  These topics start at Sec 2.1 on the webpage.  

1Al., E. O. I. B. &. (n.d.-b). Appendix B: Practice Tests (1-4) and Final Exams | Introduction to Statistics. Retrieved October 14, 2022, from https://courses.lumenlearning.com/introstats1/chapter/appendix-b-practice-tests-1-4-and-final-exams

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