How can qualitative data be expressed as numbers

The distribution can also be displayed in a pie chart, where the percentages of the colors are broken down into slices of the pie. This may be done by hand, or by using a computer program such as Microsoft Excel. If done by hand, you must find out how many degrees each piece of the pie corresponds to. Since a circle has degrees, this is found out by multiplying the relative frequencies by The respective degrees for red, orange, yellow, green, and purple in this case are , Then, use a protractor to properly draw in each slice of the pie.

Pie Chart : This pie chart shows the frequency distribution of a bag of Skittles. In statistical formulas that involve summing numbers, the Greek letter sigma is used as the summation notation. Discuss the summation notation and identify statistical situations in which it may be useful or even essential.

Many statistical formulas involve summing numbers. Fortunately there is a convenient notation for expressing summation. This section covers the basics of this summation notation.

Summation is the operation of adding a sequence of numbers, the result being their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.

The numbers to be summed called addends, or sometimes summands may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group. For finite sequences of such elements, summation always produces a well-defined sum.

Since addition is associative, the value does not depend on how the additions are grouped. Addition is also commutative, so changing the order of the terms of a finite sequence does not change its sum. There is no special notation for the summation of such explicit sequences as the example above, as the corresponding repeated addition expression will do. If, however, the terms of the sequence are given by a regular pattern, possibly of variable length, then a summation operator may be useful or even essential.

In this case the reader easily guesses the pattern; however, for more complicated patterns, one needs to be precise about the rule used to find successive terms. Informal writing sometimes omits the definition of the index and bounds of summation when these are clear from context, as in:.

One often sees generalizations of this notation in which an arbitrary logical condition is supplied, and the sum is intended to be taken over all values satisfying the condition. We can learn much more by displaying bivariate data in a graphical form that maintains the pairing of variables. Measures of central tendency, variability, and spread summarize a single variable by providing important information about its distribution.

Often, more than one variable is collected on each individual. For example, in large health studies of populations it is common to obtain variables such as age, sex, height, weight, blood pressure, and total cholesterol on each individual. Economic studies may be interested in, among other things, personal income and years of education. In the following text, we consider bivariate data, which for now consists of two quantitative variables for each individual. Our first interest is in summarizing such data in a way that is analogous to summarizing univariate single variable data.

One way to address the question is to look at pairs of ages for a sample of married couples. Bivariate Sample 1 shows the ages of 10 married couples. Going across the columns we see that husbands and wives tend to be of about the same age, with men having a tendency to be slightly older than their wives. Bivariate Sample 1 : Sample of spousal ages of 10 white American couples. These pairs are from a dataset consisting of pairs of spousal ages too many to make sense of from a table.

What we need is a way to graphically summarize the pairs of ages, such as a histogram. Each distribution is fairly skewed with a long right tail. From the first figure we see that not all husbands are older than their wives.

It is important to see that this fact is lost when we separate the variables. That is, even though we provide summary statistics on each variable, the pairing within couples is lost by separating the variables. Only by maintaining the pairing can meaningful answers be found about couples, per se. Therefore, we can learn much more by displaying the bivariate data in a graphical form that maintains the pairing. The x-axis represents the age of the husband and the y-axis the age of the wife.

Bivariate Scatterplot : Scatterplot showing wife age as a function of husband age. There are two important characteristics of the data revealed by this figure. When one variable increases with the second variable, we say that x and y have a positive association. Conversely, when y decreases as x increases, we say that they have a negative association. Second, the points cluster along a straight line. When this occurs, the relationship is called a linear relationship. The presence of qualitative data leads to challenges in graphing bivariate relationships.

We could have one qualitative variable and one quantitative variable, such as SAT subject and score. However, making a scatter plot would not be possible as only one variable is numerical. A bar graph would be possible. If both variables are qualitative, we would be able to graph them in a contingency table.

We can then use this to find whatever information we may want. In, this could include what percentage of the group are female and right-handed or what percentage of the males are left-handed. Contingency Table : Contingency tables are useful for graphically representing qualitative bivariate relationships. Privacy Policy. Skip to main content. Frequency Distributions. Search for:. Frequency Distributions for Qualitative Data.

Describing Qualitative Data Qualitative data is a categorical measurement expressed not in terms of numbers, but rather by means of a natural language description. Learning Objectives Summarize the processes available to researchers that allow qualitative data to be analyzed similarly to quantitative data. Key Takeaways Key Points Observer impression is when expert or bystander observers examine the data, interpret it via forming an impression and report their impression in a structured and sometimes quantitative form.

To discover patterns in qualitative data, one must try to find frequencies, magnitudes, structures, processes, causes, and consequences. The Ground Theory Method GTM is an inductive approach to research in which theories are generated solely from an examination of data rather than being derived deductively.

Coding is an interpretive technique that both organizes the data and provides a means to introduce the interpretations of it into certain quantitative methods.

Most coding requires the analyst to read the data and demarcate segments within it. Key Terms nominal : Having values whose order is insignificant. Interpreting Distributions Constructed by Others Graphs of distributions created by others can be misleading, either intentionally or unintentionally. Learning Objectives Demonstrate how distributions constructed by others may be misleading, either intentionally or unintentionally.

Key Takeaways Key Points Misleading graphs will misrepresent data, constituting a misuse of statistics that may result in an incorrect conclusion being derived from them. Key Terms bias : Uncountable Inclination towards something; predisposition, partiality, prejudice, preference, predilection. Graphs of Qualitative Data Qualitative data can be graphed in various ways, including using pie charts and bar charts. Learning Objectives Create a pie chart and bar chart representing qualitative data.

Key Takeaways Key Points Since qualitative data represent individual categories, calculating descriptive statistics is limited.

Mean, median, and measures of spread cannot be calculated; however, the mode can be calculated. One way in which we can graphically represent qualitative data is in a pie chart.

Categories are represented by slices of the pie, whose areas are proportional to the percentage of items in that category. Bar charts can also be used to graph qualitative data. The Y axis displays the frequencies and the X axis displays the categories. Key Terms descriptive statistics : A branch of mathematics dealing with summarization and description of collections of data sets, including the concepts of arithmetic mean, median, and mode.

Misleading Graphs A misleading graph misrepresents data and may result in incorrectly derived conclusions. Learning Objectives Criticize the practices of excessive usage, biased labeling, improper scaling, truncating, and the addition of a third dimension that often result in misleading graphs. Key Takeaways Key Points Misleading graphs may be created intentionally to hinder the proper interpretation of data, but can be also created accidentally by users for a variety of reasons.

Qualitative research focuses on the qualities of users—the 'why' behind the numbers. It's hard to conduct a successful data analysis without qualitative and quantitative data. They both have their advantages and disadvantages and often complement each other.

Quantitative data refers to any information that can be quantified — that is, numbers. If it can be counted or measured, and given a numerical value, it's quantitative in nature. Think of it as a measuring stick. Quantitative variables can tell you "how many," "how much," or "how often. How often does a customer rage click on this app?

Computers now rule statistical analytics, even though traditional methods have been used for years. When you think of statistical analysis now, you think of powerful computers and algorithms that fuel many of the software tools you use today.

Quantitative research is based on the collection and interpretation of numeric data. It focuses on measuring using inferential statistics and generalizing results. In terms of digital experience data, it puts everything in terms of numbers or discrete data —like the number of users clicking a button, bounce rates , time on site, and more.

What is the average number of times a button was dead clicked? You can use statistical operations to discover feedback patterns with any representative sample size in the data under examination. The results can be used to make predictions, find averages, test causes and effects, and generalize results to larger measurable data pools.

Unlike qualitative methodology, quantitative research offers more objective findings as they are based on more reliable numeric data. Unlike quantitative data, qualitative data is descriptive, expressed in terms of language rather than numerical values.

Qualitative data analysis describes information and cannot be measured or counted. It refers to the words or labels used to describe certain characteristics or traits. You would turn to qualitative data to answer the "why? It is often used to investigate open-ended studies, allowing participants or customers to show their true feelings and actions without guidance. Popular data collection methods are in-depth interviews, focus groups, or observation.

Qualitative research does not simply help to collect data. It gives a chance to understand the trends and meanings of natural actions. Qualitative research focuses on the qualities of users—the actions that drive the numbers.

It's descriptive research. The qualitative approach is subjective, too. Quantitative data is numbers-based, countable, or measurable. Qualitative data is interpretation-based, descriptive, and relating to language. Quantitative data tells us how many, how much, or how often in calculations.

Qualitative data can help us to understand why, how, or what happened behind certain behaviors. Quantitative data is fixed and universal. Qualitative data is subjective and unique. Quantitative research methods are measuring and counting. The power of a timeline is that it is graphical, which makes it easy to understand critical milestones, such as the progress of a project schedule.

A visualization is anything that covers data or statistics into a visual representation. Data visualizations focus more on the numbers than the design. An infographic is a visual representation of facts, events, or numbers. Infographics often combine statistics with a narrative or story.

This is a bit confusing, but one way to think about it, is that all infographics are visualizations, but not all visualizations are infographics. It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

Qualitative Search this Guide Search. Data Visualization: Quantitative vs. Qualitative Do's and Dont's Software Inspiration.