Data tables, Frequency tables, histograms, pie charts, dot plots
- What does data look like? Well often, when news programs or movies are trying to scare us with the idea of a data-driven world, they will display a screen filled with numbers, perhaps strings of ones and zeroes, waves of words, numbers and symbols. Much like a disassembled car or plane, it can be a bit ugly, confusing, and yes, scary. But, when put together the right way, this intimidating array of parts can become an attractive and functional machine, a machine that can provide us with incredible service and convenience.
Data works the same way. When organized properly, data can provide service and convenience. It can help us make good decisions quickly. It can be a tool to persuade colleagues and in doing so it can save us time and money. Similarly, imagine a world-class novel whose words have all been jumbled. It's impossible to read, it makes no sense, but put those words in the right order and the novel can tell a beautiful story.
And the incredible thing about stories is that the same story can have different meanings for different people. So, how can we organize and assemble data such that it can be useful, attractive, and interesting? More than that, how do we use data to tell thought-provoking stories? Often statisticians will use tables and graphs to tell their stories. What kind of tables and graphs? Well, let's say we have data relating to a number of adults.
In a table, we can display all the weights of these adults in pounds from heaviest to lightest. That's sort of interesting. We can also create a table that reports the frequency of each weight. In other words, how many adults weighed 170 pounds? How many weighed 130 pounds? Charts are interesting, but how about if we create a dot plot? This is very similar to our table that reported the frequency of each weight.
But, for some reason this is just more appealing and easier to consume for our eyes and brains. Still, there are so many possible values that both the chart and table can still be a bit overwhelming. How about if we grouped this data by creating 10-pound intervals? Here's what our table would look like. But we could now also use a bar graph called a histogram. As you can see, it's pretty much the same thing as our table, but again, the histogram is a bit more appealing.
One more time, back to our interval table. Let's add another column. Based on our 50 observations, we can now also report in a third column what was the relative frequency in each weight interval? As you can see, according to our chart, 10 adults weighed between 140 and 149 pounds. 10 adults of 50 adults would be 20% of all the people measured. And if you'd like, we can turn this into a relative frequency histogram.
Weight intervals define each separate bar. The height of the bar indicates the relative frequency. How about if we aren't concerned with weights? Actually, how about if we aren't measuring based on numbers? For example, let's consider the color of each person's hair. Here's the data in table form. Notice, the categories here are qualitative, different colors of hair, they are not quantitative like the weight ranges we saw before.
Here's a histogram for that hair color data. Here's one with relative frequencies, but we can also use pie charts to display this data. A circle or the whole pie represents all possible data. Each slice gives us an indication of just how many adults are in each category. So if I provide the data in this manner, an astute audience might be able to see both the frequency and the relative frequency of each hair color for the population measured.
These tables and charts are merely the tip of the iceberg. While these are some of the most common tables and charts, they are by no means the only available options. In the last decade, a group of talented and creative statisticians have started to use their skills to create incredible infographics that are interesting, colorful and sometimes even funny. So, next time you look at a chart or table, don't get intimidated, don't look for the right answer, read it like a story.
Think about what it means to you and embrace questions as an opportunity to open a discussion about the quality of the data and how the data might help you make good decisions.
Professor Eddie Davila covers statistics basics, like calculating averages, medians, modes, and standard deviations. He shows how to use probability and distribution curves to inform decisions, and how to detect false positives and misleading data. Each concept is covered in simple language, with detailed examples that show how statistics are used in real-world scenarios from the worlds of business, sports, education, entertainment, and more. These techniques will help you understand your data, prove theories, and save time, money, and other valuable resources—all by understanding the numbers.
- Calculate mean and median for specific data sets.
- Explain how the mode is used to assess a data set.
- Identify situations in which standard deviation can be used to investigate individual data points.
- Use mean and standard deviation to find the Z-score for a data point.
- List the three different categories of probability.
- Analyze data to determine if two events are dependent or independent.
- Predict possible outcomes for a situation using basic permutation calculations.
- Give examples of binomial random variables.