What Are Descriptive Statistics?

What Are Descriptive Statistics?

Let me explain descriptive statistics to you directly: they are brief coefficients that summarize a given dataset, whether it represents an entire population or just a sample. I break them down into measures of central tendency and measures of variability, or spread. Central tendency includes the mean, median, and mode, while variability covers standard deviation, variance, minimum and maximum values, kurtosis, and skewness.

Understanding Descriptive Statistics

You need to understand that descriptive statistics help describe and explain the features of a specific dataset by providing short summaries about the sample and its measures. The most common types are measures of center, like the mean, median, and mode, which you use at almost all levels of math and statistics to define and describe a dataset. For instance, you calculate the mean by adding all figures in the dataset and dividing by the number of figures.

Take this dataset: 2, 3, 4, 5, 6. The sum is 20, so the mean is 4 (20 divided by 5). The mode is the value that appears most often, and the median is the middle value separating higher from lower figures. There are less common types too, but they're still important.

People use descriptive statistics to turn hard-to-understand quantitative insights from large datasets into bite-sized descriptions. Consider a student's GPA: it averages data points from various course grades to give a general understanding of overall academic performance. Your personal GPA reflects your mean academic performance.

Important Note on Visuals

Descriptive statistics, especially in fields like medicine, often visually depict data using scatter plots, histograms, line graphs, or stem and leaf displays. I'll discuss visuals more later in this article.

Types of Descriptive Statistics

All descriptive statistics fall into measures of central tendency or measures of variability, also known as dispersion.

Central Tendency

Measures of central tendency focus on the average or middle values of datasets, while variability focuses on dispersion. These use graphs, tables, and discussions to help you understand the analyzed data.

Central tendency describes the center of a distribution. You analyze the frequency of each data point and describe it using mean, median, or mode, which capture the most common patterns.

Measures of Variability

Measures of variability analyze how dispersed the distribution is. While central tendency gives the average, it doesn't show distribution within the set.

For example, an average of 65 out of 100 doesn't reveal points at 1 and 100. Variability describes the shape and spread, with examples like range, quartiles, absolute deviation, and variance.

Consider this dataset: 5, 19, 24, 62, 91, 100. The range is 95, subtracted from the highest to the lowest.

Distribution

Distribution refers to how many times a data point occurs or fails to occur. For dataset: male, male, female, female, female, other, the distribution is 2 males, 3 females, 1 other, and 4 non-males.

Univariate vs. Bivariate

Univariate data analyzes one variable to identify characteristics of a single trait, not relationships. For example, to find the average age in a room of high school students, you gather ages and divide by the number of people.

Bivariate data links two variables for correlation. You collect two types of data and analyze their relationship, sometimes called multivariate. Say you check if older students score better on tests: gather ages and scores, then depict the relationship mathematically or graphically.

Fast Fact

Preparing and reporting financial statements are examples of descriptive statistics, while analyzing them for future decisions is inferential statistics.

Descriptive Statistics and Visualizations

Graphical representation is essential in descriptive statistics. You visualize distributions using histograms, which divide data into bins and show frequency with bars to identify shape, tendency, and variability.

Boxplots provide a summary with median, quartiles, and outliers, useful for comparing distributions across groups.

Descriptive Statistics and Outliers

Outliers are data points that differ significantly and could be errors or rare events. You detect them with boxplots, scatter plots, Z-scores, or IQR methods.

Outliers can skew measures like the mean; for dataset 1, 1, 1, 997, the mean is 250, which misrepresents. Depending on context, remove them if erroneous or keep them for insights.

Descriptive Statistics vs. Inferential Statistics

Descriptive statistics summarize data, while inferential statistics use data to make decisions or apply characteristics to others.

For a hot sauce company, sales counts and averages are descriptive. Using them to predict new product sales turns it inferential.

Explain Like I’m 5

Imagine you have a bunch of toys and want to tell friends about them without showing every one. Descriptive statistics give a quick summary so they get the idea.

What Do Descriptive Statistics Do?

They describe dataset features by generating summaries, like the ratio of men to women in a city census.

What Are Examples of Descriptive Statistics?

In baseball, they include team batting averages, runs allowed, and average wins per division.

What Is the Main Purpose of Descriptive Statistics?

To provide information about a dataset, summarizing large amounts into useful bits.

What Are the Types of Descriptive Statistics?

Frequency distribution, central tendency, and variability.

Can Descriptive Statistics Be Used to Make Inferences or Predictions?

No, they only understand historical data; inferential statistics handle interactions and predictions.

The Bottom Line

Descriptive statistics analyze, summarize, and communicate dataset findings, useful for high-level summaries like mean, median, mode, variance, range, and count, though not for decision-making.