What Are Descriptive Statistics?
Descriptive statistics are brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Measures of central tendency include the mean, median, and mode, while measures of variability include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.
Key Takeaways
- Descriptive statistics summarizes or describes the characteristics of a data set.
- Descriptive statistics consists of three basic categories of measures: measures of central tendency, measures of variability (or spread), and frequency distribution.
- Measures of central tendency describe the center of the data set (mean, median, mode).
- Measures of variability describe the dispersion of the data set (variance, standard deviation).
- Measures of frequency distribution describe the occurrence of data within the data set (count).
![Descriptive Statistics](https://www.investopedia.com/thmb/h4AO0SKvlw10q4DGLEg3373XCBg=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Descriptive_statistics-5c8c9cf1d14d4900a0b2c55028c15452.png)
Jessica Olah
Understanding Descriptive Statistics
Descriptive statistics help describe and explain the features of a specific data set by giving short summaries about the sample and measures of the data. The most recognized types of descriptive statistics are measures of center. For example, the mean, median, and mode, which are used at almost all levels of math and statistics, are used to define and describe a data set. The mean, or the average, is calculated by adding all the figures within the data set and then dividing by the number of figures within the set.
For example, the sum of the following data set is 20: (2, 3, 4, 5, 6). The mean is 4 (20/5). The mode of a data set is the value appearing most often, and the median is the figure situated in the middle of the data set. It is the figure separating the higher figures from the lower figures within a data set. However, there are less common types of descriptive statistics that are still very important.
People use descriptive statistics to repurpose hard-to-understand quantitative insights across a large data set into bite-sized descriptions. A student's grade point average (GPA), for example, provides a good understanding of descriptive statistics. The idea of a GPA is that it takes data points from a range of individual course grades, and averages them together to provide a general understanding of a student's overall academic performance. A student's personal GPA reflects their mean academic performance.
Descriptive statistics, especially in fields such as medicine, often visually depict data using scatter plots, histograms, line graphs, or stem and leaf displays. We'll talk more about visuals later in this article.
Types of Descriptive Statistics
All descriptive statistics are either measures of central tendency or measures of variability, also known as measures of dispersion.
Central Tendency
Measures of central tendency focus on the average or middle values of data sets, whereas measures of variability focus on the dispersion of data. These two measures use graphs, tables, and general discussions to help people understand the meaning of the analyzed data.
Measures of central tendency describe the center position of a distribution for a data set. A person analyzes the frequency of each data point in the distribution and describes it using the mean, median, or mode, which measures the most common patterns of the analyzed data set.
Measures of Variability
Measures of variability (or measures of spread) aid in analyzing how dispersed the distribution is for a set of data. For example, while the measures of central tendency may give a person the average of a data set, it does not describe how the data is distributed within the set.
So while the average of the data might be 65 out of 100, there can still be data points at both 1 and 100. Measures of variability help communicate this by describing the shape and spread of the data set. Range, quartiles, absolute deviation, and variance are all examples of measures of variability.
Consider the following data set: 5, 19, 24, 62, 91, 100. The range of that data set is 95, which is calculated by subtracting the lowest number (5) in the data set from the highest (100).
Distribution
Distribution (or frequency distribution) refers to the number of times a data point occurs. Alternatively, it can be how many times a data point fails to occur. Consider this data set: male, male, female, female, female, other. The distribution of this data can be classified as:
- The number of males in the data set is 2.
- The number of females in the data set is 3.
- The number of individuals identifying as other is 1.
- The number of non-males is 4.
Univariate vs. Bivariate
In descriptive statistics, univariate data analyzes only one variable. It is used to identify characteristics of a single trait and is not used to analyze any relationships or causations.
For example, imagine a room full of high school students. Say you wanted to gather the average age of the individuals in the room. This univariate data is only dependent on one factor: each person's age. By gathering this one piece of information from each person and dividing by the total number of people, you can determine the average age.
Bivariate data, on the other hand, attempts to link two variables by searching for correlation. Two types of data are collected, and the relationship between the two pieces of information is analyzed together. Because multiple variables are analyzed, this approach may also be referred to as multivariate.
Let's say each high school student in the example above takes a college assessment test, and we want to see whether older students are testing better than younger students. In addition to gathering the ages of the students, we need to find out each student's test score. Then, using data analytics, we mathematically or graphically depict whether there is a relationship between student age and test scores.
Note
The preparation and reporting of financial statements is an example of descriptive statistics. Analyzing that financial information to make decisions on the future is inferential statistics.
Descriptive Statistics and Visualizations
One essential aspect of descriptive statistics is graphical representation. Visualizing data distributions effectively can be incredibly powerful, and this is done in several ways.
Histograms are tools for displaying the distribution of numerical data. They divide the data into bins or intervals and represent the frequency or count of data points falling into each bin through bars of varying heights. Histograms help identify the shape of the distribution, central tendency, and variability of the data.
Another visualization is boxplots. Boxplots, also known as box-and-whisker plots, provide a concise summary of a data distribution by highlighting key summary statistics including the median (middle line inside the box), quartiles (edges of the box), and potential outliers (points outside, or the "whiskers"). Boxplots visually depict the spread and skewness of the data and are particularly useful for comparing distributions across different groups or variables.
Descriptive Statistics and Outliers
Whenever descriptive statistics are being discussed, it's important to note outliers. Outliers are data points that significantly differ from other observations in a dataset. These could be errors, anomalies, or rare events within the data.
Detecting and managing outliers is a step in descriptive statistics to ensure accurate and reliable data analysis. To identify outliers, you can use graphical techniques (such as boxplots or scatter plots) or statistical methods (such as Z-score or IQR method). These approaches help pinpoint observations that deviate substantially from the overall pattern of the data.
The presence of outliers can have a notable impact on descriptive statistics, skewing results and affecting the interpretation of data. Outliers can disproportionately influence measures of central tendency, such as the mean, pulling it towards their extreme values. For example, the dataset of (1, 1, 1, 997) is 250, even though that is hardly representative of the dataset. This distortion can lead to misleading conclusions about the typical behavior of the dataset.
Depending on the context, outliers can often be treated by removing them (if they are genuinely erroneous or irrelevant). Alternatively, outliers may hold important information and should be kept for the value they may be able to demonstrate. As you analyze your data, consider the relevance of what outliers can contribute and whether it makes more sense to just strike those data points from your descriptive statistic calculations.
Descriptive Statistics vs. Inferential Statistics
Descriptive statistics have a different function from inferential statistics, which are data sets that are used to make decisions or apply characteristics from one data set to another.
Imagine another example where a company sells hot sauce. The company gathers data such as the count of sales, average quantity purchased per transaction, and average sale per day of the week. All of this information is descriptive, as it tells a story of what actually happened in the past. In this case, it is not being used beyond being informational.
Now let's say that the company wants to roll out a new hot sauce. It gathers the same sales data above, but it uses the information to make predictions about what the sales of the new hot sauce will be. The act of using descriptive statistics and applying characteristics to a different data set makes the data set inferential statistics. We are no longer simply summarizing data; we are using it to predict what will happen regarding an entirely different body of data (in this case, the new hot sauce product).
What Is Descriptive Statistics?
Descriptive statistics is a means of describing features of a data set by generating summaries about data samples. For example, a population census may include descriptive statistics regarding the ratio of men and women in a specific city.
What Are Examples of Descriptive Statistics?
In recapping a Major League Baseball season, for example, descriptive statistics might include team batting averages, the number of runs allowed per team, and the average wins per division.
What Is the Main Purpose of Descriptive Statistics?
The main purpose of descriptive statistics is to provide information about a data set. In the example above, there are dozens of baseball teams, hundreds of players, and thousands of games. Descriptive statistics summarizes large amounts of data into useful bits of information.
What Are the Types of Descriptive Statistics?
The three main types of descriptive statistics are frequency distribution, central tendency, and variability of a data set. The frequency distribution records how often data occurs, central tendency records the data's center point of distribution, and variability of a data set records its degree of dispersion.
Can Descriptive Statistics Be Used to Make Inferences or Predictions?
Technically speaking, descriptive statistics only serves to help understand historical data attributes. Inferential statistics—a separate branch of statistics—is used to understand how variables interact with one another in a data set and possibly predict what might happen in the future.
The Bottom Line
Descriptive statistics refers to the analysis, summary, and communication of findings that describe a data set. Often not useful for decision-making, descriptive statistics still hold value in explaining high-level summaries of a set of information such as the mean, median, mode, variance, range, and count of information.