How to use tables, graphs, and charts

Study guide: Tables, bar charts, line graphs, pie charts, and stem-and-leaf plots

Introduction

Welcome to your study guide on different kinds of graphs and charts! In this guide, you will learn about tables, bar charts, line graphs, pie charts, and stem-and-leaf plots. These tools help us organize information (data) so we can understand it better, compare things, and explain our ideas clearly. Whether you're checking out a sports statistic, reading a weather report, or even looking at your school grades, graphs and charts are there to help you make sense of the numbers.

Why should we learn about graphs and charts?

Organization: They help arrange lots of numbers and facts in a neat and clear way.

Analysis: Graphs let us see patterns, trends, and differences quickly. For example, you can see if something is increasing, decreasing, or staying the same

Explanation: They make it easier to share and explain information to others. A picture (or graph) often tells the story better than a long list of numbers!

Imagine a chef checking which dish is most popular or a coach looking at players' scores. In each job, clear graphs and charts help professionals make better decisions.

1. Tables

What they are: Tables use rows and columns to organize data. Think of a table like a grid where each cell holds a piece of information.

Why they’re useful: Tables let you look up specific numbers quickly. They are great for listing information like class test scores, a schedule of events, or even a menu.

Real-world example: In a school, a teacher might use a table to show students' names alongside their test scores. In a grocery store, a price list in a table helps you find how much each product costs.

2. Bar charts

What they are: Bar charts use bars (either vertical or horizontal) to show how different groups compare to each other.

Why they’re useful: They make it easy to compare the size or amount of different groups at a glance.

Real-world example: A sports team might use a bar chart to compare the number of goals scored by each player. In business, a bar chart can show sales numbers for different products.

3. Line graphs

What they are: Line graphs use points connected by lines to show changes over time.

Why they’re useful: They are perfect for showing trends, like rising or falling temperatures, over days, months, or even years.

Real-world example: Weather stations use line graphs to show changes in temperature during the week. Scientists use line graphs to track changes in plant growth over time.

4. Pie charts

What they are: Pie charts are circular graphs divided into slices. Each slice shows a part of the whole.

Why they’re useful: They help you see how a total amount is split into different parts, making it easy to see proportions.

Real-world example: In a classroom, a pie chart might show the percentage of students who prefer different types of snacks. Businesses use pie charts to see what percentage of their sales comes from each product.

5. Stem-and-leaf plots

What they are: A stem-and-leaf plot is a way to display data where numbers are split into a “stem” (the first digit or digits) and a “leaf” (the last digit).

Why they’re useful: This plot shows how data is distributed and helps you see the shape of the data (for example, whether most numbers are grouped together or spread out).

Real-world example: A teacher might use a stem-and-leaf plot to display the distribution of scores on a test. This makes it easier to see if many students scored similarly or if there was a wide range of scores.

How graphs and charts help in different jobs and careers

• Business: Managers use bar charts and pie charts to track sales, compare products, and plan for the future.
• Science: Researchers use line graphs to study trends like temperature changes or population growth.
• Healthcare: Doctors and nurses use line graphs to monitor patients’ vital signs, like heart rate or blood pressure, over time.
• Sports: Coaches use bar charts and line graphs to analyze players’ performance and strategize for upcoming games.
• Education: Teachers use tables and stem-and-leaf plots to record and review student progress and test scores.

Conclusion

Graphs and charts are more than just pictures - they are powerful tools that help us make sense of the world around us. By learning how to create and interpret tables, bar charts, line graphs, pie charts, and stem-and-leaf plots, you gain skills that are useful in school and many jobs. They help you organize data, spot trends, compare information, and explain your findings clearly.

So, next time you see a graph or chart, remember: you’re looking at a clever way to understand and share important information. Happy graphing!

The limits of mean, median, mode, and range

Study guide: Understanding the limits of basic statistical methods

Now that we are familiar with basic statistical methods like mean, median, mode, and range, we are going to learn about their limits. In other words, while these methods may potentially tell us a lot about something, they may also fall short in being able to explain the complete picture of a situation. There may be other underlying causes, effects, and possible alternative explanations at play that these methods, alone, can’t get to the heart of. Let’s briefly review what these methods are, and then we’ll get into discussing when they are useful and when they might not tell us the whole story.

1. Mean (average)

What It Is:

The mean is what you get when you add up all the numbers in a set and then divide by how many numbers there are.

When It’s Useful:

Example: Imagine you want to find the average score on a math test. If you add all the test scores together and divide by the number of students, you get the mean score. This helps you know the overall performance of the class.

Limitations:

The mean can be affected by really high or really low numbers (called outliers).

Example: Suppose most students scored around 80, but one student scored 20. The mean might drop significantly, giving the impression that the class did worse than it really did. In situations like incomes, a few very high salaries can make the mean much higher than what most people earn.

2. Median (middle value)

What It Is:

The median is the middle number in a list of numbers that have been arranged in order.

When It’s Useful:

Example: If you arrange the ages of children in a classroom from youngest to oldest, the median age tells you the middle age. This is good when you have numbers that might be very high or very low, because the median won’t be as affected by them as the mean is.

Limitations:

The median only shows one value and does not give any information about the other numbers.

Example: If you know the median income of a group of people, you still don’t know if there are lots of people who earn much more or much less than that median income.

3. Mode (most frequent value)

What It Is:

The mode is the number that appears most often in a set of numbers.

When It’s Useful:

Example: If a teacher wants to know which test score was most common, the mode will tell you which score happened the most. This can help show what most students did on the test.

Limitations:

There might be no mode at all if no number repeats. Sometimes, a data set can have more than one mode, and that can be confusing.

Example: In a survey about favorite ice cream flavors, if two flavors are equally popular, then there are two modes. This might not give a clear answer about which flavor is the overall favorite.

4. Range (difference between the highest and lowest)

What It Is:

The range is the difference between the largest and the smallest numbers in a set.

When It’s Useful:

Example: If you look at the temperatures during a week, the range tells you how much the temperature changed from the coldest to the hottest day.

Limitations:

The range only considers two numbers (the highest and lowest) and ignores everything in between.

Example: Two classes might have the same range of test scores, but one class might have most students scoring around the middle, while the other class has scores spread out. The range alone wouldn’t show these differences.

Real-world situations: Where they work and where they fall short

Test Scores in a Class:

• Useful: The mean gives a quick idea of how well the class did on average.
• Falls Short: A few very low or very high scores can distort the mean. The median might be better if the scores are very spread out.

House Prices in a Neighborhood:

• Useful: The mean or median can tell you about the general cost of houses.
• Falls Short: A few extremely expensive houses can make the mean much higher than what most people pay. The median might hide how varied the prices really are.

Favorite Foods Survey:

• Useful: The mode shows which food is most popular among the respondents.
• Falls Short: If people have many different favorite foods and no food is chosen often, the mode might not tell you much about overall preferences.

Sports Statistics:

• Useful: A player’s average score (mean) can show their overall performance.
• Falls Short: The mean might hide important details like a few games where the player scored very low, even though they usually scored high. Looking at the range or the list of scores can give more insight.

Why knowing the limits is important

• Incomplete Picture: Each statistic gives us just one view of the data. They can help us summarize information quickly, but they don’t always show everything.
• Outliers: Extreme values (very high or very low numbers) can change the mean and range, but might not affect the median as much.
• Different Stories: Two sets of numbers can have the same mean or range but tell very different stories about the data.

By understanding the limits of mean, median, mode, and range, you can learn to look at data in more than one way. Sometimes, you might need to use several of these tools together to get a complete picture of what the numbers are really telling you.

Remember, statistics are like different tools in a toolbox. No single tool can do all the work, so it’s important to know which one to use and when to use another one for a better understanding.

How to calculate mean, median, mode, and range

Statistics Made Simple: A study guide for sixth graders on mean, median, mode, and range

Welcome, young mathematicians! In this guide, we’ll explore four important ideas in statistics: mean, median, mode, and range. These ideas help us understand groups of numbers and are useful in many careers such as medicine, nursing, education, business, the social sciences, the natural sciences, accounting, and more. Let’s learn what each term means, how to find them, and practice with fun problems!

Why learn these statistical methods?

Imagine you’re a scientist studying how much rain falls in different parts of the country, or a business person trying to figure out the average sales in your store. By knowing mean, median, mode, and range, you can:

• Summarize lots of data with just a few numbers.
• Make good decisions based on data.
• Compare different groups easily.
• Use these skills in many real-world jobs like medicine (to analyze patient data), nursing (to understand vital statistics), education (to see test score trends), and even accounting (to track financial information), to name just a few.

By practicing these skills now, you’re building a foundation that will help you solve real-world problems later in life!

Mean (average)

What is the mean?

Definition: The mean is the average of a set of numbers.

How to Find It: Add up all the numbers, then divide the total by the number of numbers.

Example: Find the mean of these numbers: 4, 8, 10, 6

• Step 1: Add them up: 4 + 8 + 10 + 6 = 28
• Step 2: Count how many numbers there are: There are 4 numbers.
• Step 3: Divide the total by the count: 28 ÷ 4 = 7
• The mean is 7.

Practice Problems (try these yourself!):

• Problem 1: Find the mean of: 3, 5, 7, 9, 11
• Problem 2: Find the mean of: 10, 20, 30, 40
• Problem 3: What is the mean of: 2, 4, 6, 8, 10, 12?

Median (middle number)

What is the median?

Definition: The median is the middle number in a list when the numbers are arranged in order (from smallest to largest).

How to Find It:

• 1. Arrange the numbers in order.
• 2. If there’s an odd number of numbers, the median is the middle one.
• 3. If there’s an even number of numbers, the median is the average of the two middle numbers.

Example 1 (odd number of items): Find the median of: 3, 1, 4, 5, 2

• Step 1: Arrange in order: 1, 2, 3, 4, 5
• Step 2: The middle number is the 3rd number (since there are 5 numbers): Median = 3

Example 2 (even number of items): Find the median of: 7, 3, 9, 1

• Step 1: Arrange in order: 1, 3, 7, 9
• Step 2: There are 4 numbers (even), so take the average of the 2 middle numbers (3 and 7): Median = (3 + 7) ÷ 2 = 10 ÷ 2 = 5

Practice Problems:

• Problem 1: Find the median of: 8, 3, 5, 12, 10
• Problem 2: Find the median of: 4, 8, 15, 16, 23, 42
• Problem 3: What is the median of: 11, 7, 9, 3, 5, 13?

Mode (most frequent number)

What is the mode?

Definition: The mode is the number that appears most often in a set.

How to Find It: Look at the list of numbers and count which one appears the most times.

Example: Find the mode of: 2, 4, 4, 6, 8, 4, 10

• Step 1: Count how many times each number appears:

   - 2 appears once.
   - 4 appears three times.
   - 6 appears once.
   - 8 appears once.
   - 10 appears once.

• Step 2: The number 4 appears the most, so Mode = 4

Practice Problems:

• Problem 1: Find the mode of: 1, 2, 2, 3, 4, 2, 5
• Problem 2: What is the mode of: 7, 7, 8, 9, 10, 7, 8, 9?
• Problem 3: Identify the mode of: 3, 3, 6, 9, 9, 9, 12

Range (difference between highest and lowest)

What is the range?

Definition: The range is the difference between the highest and lowest numbers in a set.

How to Find It:

• 1. Identify the largest and smallest numbers.
• 2. Subtract the smallest from the largest.

Example: Find the range of: 5, 12, 3, 9, 7

• Step 1: Identify the smallest number (3) and the largest number (12).
• Step 2: Subtract: 12 - 3 = 9
• The range is 9.

Practice Problems:

• Problem 1: Find the range of: 10, 15, 20, 25, 30
• Problem 2: What is the range of: 3, 8, 12, 7, 6?
• Problem 3: Calculate the range for: 2, 2, 2, 2, 2

Real-world applications

Why are these skills important?

• Medicine & Nursing: Doctors and nurses use averages (means) to understand patient test results, like blood pressure readings or temperatures.
• Education: Teachers analyze test scores (using medians and modes) to see how students are performing.
• Business & Accounting: Companies use the mean to determine average sales, and the range to understand fluctuations in prices.
• Social & Natural Sciences: Researchers use these statistics to study trends and differences in data, such as population growth or environmental changes.

By practicing these skills now, you’re building a foundation that will help you solve real-world problems later in life. Whether you become a doctor, a teacher, an accountant, a scientist, or an entrepreneur, understanding statistics is a powerful tool!

Final thoughts

Keep practicing these concepts, and soon calculating the mean, median, mode, and range will feel like second nature. These skills are not just for your math class - they help you make sense of the world by turning numbers into useful information. Whether you're comparing test scores, planning a budget, or analyzing scientific data, you'll be ready to tackle the challenge!

Giorgi’s descriptive phenomenological method

A brief overview of data collection using Giorgi’s descriptive phenomenological method in psychology

Prepared by Aaron S. Robertson, MSM, February 2018

What:

• Developed by Amedeo Giorgi, currently at Saybrook University in California.
• Has its roots primarily in the research approach of German philosopher Edmund Husserl (1859-1938).
• Husserl founded the movement of phenomenology, which, according to Wikipedia (n.d.), “…is the philosophical study of the structures of experience and consciousness” (para. 1).
• “Phenomenology seeks to make explicit the implicit structure and meaning of human experiences. It is the search for ‘essences’ that cannot be revealed by ordinary observation” (Sanders, 1982, p. 354).
• Four rigorous scientific criteria to be met, according to Giorgi: methodical, systematic, general, and critical (Applebaum, 2011; Englander, 2012).
• Giorgi seeks a shift from psychology as a natural science to that of a human science (Applebaum, 2011).

Some Main Features:

• Interviews or submitted written descriptions
• Interviews can take as long as 1-2 hours
• At least three interviews needed
• Submitted written descriptions arguably more ideal for undergraduate research or as material for workshops, but written descriptions can also be more concise, which may make it possible for the researcher to more easily solicit the experiences and insights of more participants
• A pre-interview meeting with participants is reasonable and within the realm of possibility
• While quantitative research looks for measurement by asking, “How many?”, this method is looking for meaning by asking, “What is it like?”
• Pursuing “depth” over “sampling” (Source: Englander, 2012)

Bibliography

Applebaum, M. H. (2011). Amedeo Giorgi and psychology as a human science. Neuroquantology, 9(3), 518-525.

Englander, M. (2012). The interview: Data collection in descriptive phenomenological human scientific research. Journal of Phenomenological Psychology, 43(1), 13-35. doi:10.1163/156916212X632943

Giorgi, A. (2006). Concerning variations in the application of the phenomenological method. The Humanistic Psychologist, 34(4), 305–319.

Giorgi, A. (2009). The descriptive phenomenological method in psychology: A modified Husserlian approach. Pittsburgh, PA: Duquesne University Press.

Giorgi, A. (1997). The theory, practice, and evaluation of the phenomenological method as a qualitative research procedure. Journal of Phenomenological Psychology, 28, 235–260.

Phenomenology (philosophy). (n.d.). In Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Phenomenology_(philosophy)

Sanders, P. (1982). Phenomenology: A new way of viewing organizational research. Academy of Management Review, 7(3), 353-360.

Selected Quotes from Bibliography Sources:

“In order for phenomenological research to achieve the same rigorous quality as natural scientific research, it is important that the research process be methodologically articulated in such a manner that data collection and data analysis are both seen as part of a single, unified process with the same underlying theory of science. Hence, if one is following Husserlian descriptive phenomenological philosophy as a basis for a phenomenological theory of science, both the data collection and the data analysis need to follow descriptive phenomenology in order to achieve rigor. Of course, one can do qualitative research in other ways, but in order to meet all the criteria of science, one needs to consider the consistency of method following the same logic that is part of the same theory of science.” (Englander, 2012, pp. 15-16)

“…it is essential to understand that one needs to adopt a different strategy when doing science in contrast to doing philosophy (Giorgi, 1997, 2006, 2009). In other words, one cannot just take a philosophical method and use it for scientific purposes, because a philosophical method is developed for philosophical purposes, not scientific ones (Giorgi, 1997, 2009).” (Englander, 2012, p. 16)

“The phenomenological method in human science recommends that one uses at least three participants, obviously not because that the number three corresponds with a statistical analysis but because one or two subjects would be too difficult for the researcher to handle in terms of their own imagination (Giorgi, 2009). Although we are not interested in “how many?” who have had a particular experience, for the purpose of comparison, we could take note on how many times the phenomenon makes its presence in the description (Giorgi, 2009, p. 198).” (Englander, 2012, p. 21)

“As Giorgi (2009, pp. 198–199) points out, ‘Research based upon depth strategies should not be confused with research based upon sampling strategies’” (Englander, 2012, p. 21).

“In general, descriptive phenomenological psychology, using a qualitative method, tries to identify the essential structure of a phenomenon. The process of selecting the participants and number of participants differ from mainstream natural scientific psychology mainly due to that the method rest upon a different theory of science and thus signifies a different epistemological purpose.” (Englander, 2012, p. 23).

“…in order to fulfill the meaning of science, human subjectivity is to be investigated by means of a firmly grounded, methodical, general, and disciplinary attitude capable of making substantial contributions to the scientific community’s growing body of knowledge. Thus for Giorgi both the “human” and the “scientific” dimensions of human science are essential constituents if qualitative psychology is to represent a genuine alternative to the dominant, empirical paradigm.” (Applebaum, 2011, p. 520)