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Displaying Statistical Data

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Displaying Statistical Data

You’ve just designed the perfect research experiment to test the relationship between social media use and productivity. You made sure you used random sampling and did your best to control for variables. Now, you are ready to interpret the data you have gathered. But where do you start? One of the best ways to understand and interpret data is by using methods of displaying statistical data.

  • In this article, we will begin with an overview of the methods of displaying statistical data.
  • Then, we will discuss the most traditional way of displaying numerical statistics.
  • As we move along, we will dive into several types of graphical displays of statistical data.
  • We will explain the best way to display statistics of data that varies over time.
  • Finally, we will understand how to determine the best way to display statistical data.

Methods of Displaying Statistical Data

The most basic way of presenting statistical data is through text. There are many benefits to using this format. You are able to go into more depth to describe and contextualize your findings. You can explain what each variable is and how other elements are controlled for. However, displaying statistical data offers a visual element to interpreting data. Especially if you have received a lot of information, displaying statistical data can help you mentally organize your findings.

Data are a set of facts that only paint a partial picture of reality.

However, by using analysis and displaying statistical data, we can begin to fill in some of the gaps. There are two primary methods of displaying statistical data: tabular form and graphical form.

Tabular form displays statistical data by using tables (i.e. frequency tables).

Graphical form displays statistical data by using graphs (i.e. scatter plots).

Displaying Numerical Data Statistics

Let's begin by taking a look at a few basic ways of displaying numerical data statistics.

Tables

One of the oldest ways of displaying numerical data statistics is through tables. This may be due to the fact that tables are easy to understand. Generally, if you know how to read, you can understand the information on a table without any prior training.

Tables use rows and columns to convey information in a data set into words or numbers.

Tables are also the most appropriate option for displaying individual information. This way all the information can be seen rather than grouped together or generalized like many graphical forms of displaying statistical data. For example, if the result for one data point is 65.489, you can simply write that into the table. However, in other forms of displaying statistical data, you may have to round that number to 65 or, you may not even see what the number is at all.

Tables are also great for comparing quantitative information between different variables. Take the following as an example.

Displaying Statistical Data, table showing percentages, StudySmarterTable comparing variables, commons.wikimedia.org

A common type of table is called a frequency table. Frequency is simply how often a specific finding occurs. There are several types of frequencies a frequency table can display as well: relative frequency and……

Displaying Statistical Data, frequency table, StudySmarterFrequency table, commons.wikimedia.org

While tables can be incredibly useful in presenting a large number of numerical data statistics, there are downsides. One major downside to using tables is that it can take a long time to interpret the data. Sometimes, there is so much information, it can be difficult to see any data trends that may be occurring. For this reason, graphical forms of displaying statistical data are especially useful.

Pie Chart

Another great way of visually displaying statistical data is by using a pie chart. A pie chart is generally used to nominal data (or, in other words, different categories of data). Usually, a pie chart should only be used to represent only a small number of categories but can still be a great way to summarize a large amount of data.

Take the following pie chart demonstrating the percentage of different races in America.

Displaying Statistical Data, race in America pie chart, SRace in America, commons.wikimedia.org

The one downfall of a pie chart is that there is no way to know the results of individual data. Results from each category are grouped together to form a broad picture of the results. Also, pie charts do not offer any information regarding outliers, means, medians, or any other summary information that may aid in analyzing the results of your research.

Graphical Display of Statistical Data

Graphs come in handy when displaying statistical data because they often simplify complex information by using images and highlighting data trends. They are useful for explaining, summarizing, and exploring the quantitative data we collect in our research. Graphical displays of statistical data can also come in handy because they can present large amounts of data. If you have just collected thousands of data points from your research, it would be unrealistic to display each point on a table.

Also, finding a way to categorize the information onto a table may erase any statistical trends you are trying to uncover. Let’s take a look at a few types of graphical displays of statistical data including a box and whiskers chart, bar graphs and histograms, and scatter plots.

Box and Whisker Plot

A very basic way to graphically display statistical data is with a box and whisker plot. When analyzing a data set, one of the first things researchers will do is summarize the data. A box and whisker plot includes a five-number summary:

  • Minimum: the smallest value in the data set

  • First quartile: the lower 25% of the data set

  • Medium: the middle value in the data set

  • Third quartile: the upper 25% of the data set

  • Maximum: the largest value in the data set

The rectangle represents the first quartile, median, and third quartile. The lines or whiskers extend to the minimum and maximum values in the data set. Sometimes, there you may get results that are way outside of the other results in the data set. These are called outliers and are usually represented by a single point outside of the box and whisker plot and are not considered the minimum or maximum value.

Displaying Statistical Data, box and whisker chart of countries, StudySmarterBox and whisker plot, commons.wikimedia.org

Box and whisker plots are a great way to visually display a summary of your findings. It can also be useful in comparing multiple data sets, evaluating how one data set changes over time, or seeing how the data set has changed before and after an experiment.

Bar Graph and Histogram

Bar graphs and histograms are also commonly used methods of displaying statistical data.

Bar graphs and histograms use horizontal or vertical bars to compare values in several categories or groups.

The bar height or length indicates the amount of information in that category. You can use any measurement parameters you'd like such as frequency or mean. Bar graphs and histograms are very similar but there are a few ways in which they differ? For one, histograms show the value of a range of categories or data points while bar graphs show just one. Additionally, the bars on bar graphs are separated while the bars on histograms are always touching.

Displaying Statistical Data, bar graph of male age of incarceration, StudySmarterBar graph, commons.wikimedia.orgDisplaying Statistical Data, histogram, StudySmarterHistogram, commons.wikimedia.org

For example, if you are wanting to make a bar graph of how many people in your senior class have birthdays in each month, you would make a separate bar for each month. However, if you wanted to make a histogram, you would look at how many people in your senior class have birthdays in a range of months (i.e. Jan-Mar, Apr-Jun, Jul- Sept, Oct-Dec).

Bar graphs and histograms can be especially helpful in analyzing data because they can visually show trends within the data that other graphs such as pie charts cannot.

Scatter Plot

Finally, one of the most effective ways of displaying statistical data is with a scatter plot. Scatter plots allow you to display all the values in your data set represented by a single dot on the graph. The x- and y-axes represent the two variables you are investigating. Once all the data is plotted, you will be able to see if there is an association between those two variables. This association is commonly referred to as correlation.

A negative correlation occurs when higher values on one variable are associated with lower values on a second variable.

A positive correlation means that higher values on one variable are associated with higher values on a second variable.

In psychology, researchers are always looking for a correlation between variables. Finding a correlation between variables can lead to important discoveries and a better understanding of the human mind and behavior.

For example, they may want to see if there is a correlation between hours of sleep and school performance (GPA). In this case, the x-axis might represent the hours of sleep a person gets at night and the y-axis might represent that person's GPA.

If the correlation isn't immediately clear, a correlation regression line can be calculated which can then be plotted to show correlation. It is important to note, however, that there may not always be a correlation between variables.

Displays Statistics of Data That Varies Over Time

Sometimes, researchers want to observe how a variable changes over time. The best way to visually display statistics of data that varies over time is by using a line graph. Line graphs use a single dot to indicate a data point. Then, a straight line is drawn to connect each dot on the graph. This will visually show any increases or decreases (if any) between each time interval. Line graphs also show any broader trends over an extended amount of time. The x-axis is usually time and the y-axis is the variable you are investigating.

A great way to show changes in population over time is by using a line graph.

Displaying Statistical Findings, line graph of population over time, StudySmarterLine graph, commons.wikimedia.org

While a line graph is the best way to show changes over time, it can also be helpful in showing other types of continuous variables such as distance. Line graphs are usually best for smaller data sets.

Best Way to Display Statistical Data

Now that we've briefly discussed the ways of displaying statistical data, how do you decide which methods are the best way to display statistical data? Several factors should be considered while making this decision including:

  • simplicity of presentation

  • the data format

  • the method of analysis you plan to use

  • the information you want to emphasize

  • the amount of information in your data set

Displaying Statistical Data - Key takeaways

  • There are two primary methods of displaying statistical data: tabular form and graphical form.
  • One of the oldest ways of displaying numerical data statistics is through tables. Tables use rows and columns to convey information in a data set into words or numbers.
  • Afew types of graphical displays of statistical data including a box and whiskers chart, bar graphs and histograms, and scatter plots.
  • The best way to visually display statistics of data that varies over time is by using a line graph.
  • Several factors should be considered while making this decision including:
    • simplicity of presentation
    • the data format

    • the method of analysis you plan to use

    • the information you want to emphasize

    • the amount of information in your data set

Frequently Asked Questions about Displaying Statistical Data

Several factors should be considered while deciding how to display statistical data:

  • simplicity of presentation

  • the data format

  • the method of analysis you plan to use

  • the information you want to emphasize

  • the amount of information in your data set  

Three ways of graphically displaying data in statistics include box and whiskers charts, bar graphs and histograms, and scatter plots.

There are two primary methods of displaying statistical data: tabular form and graphical form.

The best way to display quantitative data over time is by using a line graph. 

Some of the best methods of visually displaying statistical data is with bar graphs and histograms, pie charts, line graphs, and scatter plots. 

Final Displaying Statistical Data Quiz

Question

What is a scatter plot?

Show answer

Answer

A graph that shows the relationship between two variables

Show question

Question

When is a scatter plot used in psychology?

Show answer

Answer

Correlational research/studies

Show question

Question

How do you read a scatter plot?

Show answer

Answer

From left to right!

Show question

Question

What is the line of best fit?

Show answer

Answer

A line that shows the relationship between the two variables (and best summarizes the data)

Show question

Question

Does the line of best fit go through all the points?

Show answer

Answer

Yes

Show question

Question

Does the line of best fit have to be straight?

Show answer

Answer

Yes, it's a line

Show question

Question

What relationship between the variables does a positive scatter plot show?

Show answer

Answer

Both variables increase

Show question

Question

What relationship between the variables does a negative scatter plot show?

Show answer

Answer

One variable increases and one decreases

Show question

Question

The slope of line of best fit for a positive scatter plot would be ___________

Show answer

Answer

Positive

Show question

Question

The slope of line of best fit for a negative scatter plot would be ___________


Show answer

Answer

Positive

Show question

Question

What does a scatter plot with no relationship look like?

Show answer

Answer

The points are scattered all around the graph

Show question

Question

What does a scatter plot with no relationship mean?

Show answer

Answer

There is no relationship between the two variables being studied

Show question

Question

What type of scatter plot would this example have: 

Food eaten and weight gained

Show answer

Answer

Positive

Show question

Question

What type of scatter plot would this example have: 

Temperature and clothes worn

Show answer

Answer

Positive

Show question

Question

What type of scatter plot would this example have: 

Body muscle and intelligence

Show answer

Answer

Positive

Show question

Question

What is the best way to display statistical data over time? 

Show answer

Answer

Line graph

Show question

Question

_________ are a set of facts that only paint a partial picture of reality. 

Show answer

Answer

Data

Show question

Question

What are the two primary methods of displaying statistical data? 

Show answer

Answer

Tabular form and graphical form

Show question

Question

_________ use rows and columns to convey information in a data set into words or numbers. 


Show answer

Answer

Tables

Show question

Question

Which way of displaying statistical data is best for displaying specific individual information? 


Show answer

Answer

Table

Show question

Question

What is a major disadvantage of using tables to display statistical findings? 


Show answer

Answer

One major downside to using tables is that it can take a long time to interpret the data. Sometimes, there is so much information, it can be difficult to see any data trends that may be occurring.

Show question

Question

True or False? Pie charts are a great way of displaying individual information. 

Show answer

Answer

False

Show question

Question

Graphs come in handy when displaying statistical data because they often _________ complex information by using images and highlighting data trends.

Show answer

Answer

simplify

Show question

Question

What does the first quartile of a box and whisker plot represent? 


Show answer

Answer

the lower 25% of the data set

Show question

Question

True or False? Box and whisker plots can be used in comparing multiple data sets. 

Show answer

Answer

True

Show question

Question

______________ use horizontal or vertical bars to compare values in several categories or groups.

Show answer

Answer

Bar graphs and histograms

Show question

Question

What is the difference between histograms and bar graphs? 


Show answer

Answer

Histograms show the value of a range of categories or data points while bar graphs show just one. Additionally, the bars on bar graphs are separated while the bars on histograms are always touching.

Show question

Question

A ______________ occurs when higher values on one variable are associated with lower values on a second variable.

Show answer

Answer

negative correlation

Show question

Question

A positive correlation means that higher values on one variable are associated with higher values on a second variable.

Show answer

Answer

Positive correlation

Show question

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