What are Descriptive Statistics?
Descriptive statistics summarize the properties of a dataset using summary statistics, tables, and graphs. These descriptions characterize vital information about the variables, their relationships, and trends. Ideally, they provide a clearer picture of the data than the raw values. In short, they describe the essential features of a sample.
The primary purpose of descriptive statistics is for analysts to communicate a brief, straightforward overview of the data to others, making the data accessible to a broader group of stakeholders. A nicely organized presentation allows others to gain insights quickly without requiring them to assess the raw data. Frequently, they are the foundation for understanding a dataset and can lead to additional analyses and decision-making.
For example, we can describe starting salaries of college majors by calculating the mean salary and the range for each type of major. We can also describe the percentage of college graduates by major who obtain jobs within six months of graduation.
Crucially, descriptive statistics apply only to the sample and do not generalize outside it. To generalize the results to a population, you must use inferential statistics instead.
Statisticians typically break them down to univariate and bivariate measures. Let’s dig into the different types!
Learn more about Descriptive vs. Inferential Statistics.
Univariate Descriptive Statistics
Univariate statistics describe a single variable independently of other variables. Typically, analysts present descriptive statistics that summarize a variable’s central tendency, variability, and distribution properties.
The central tendency describes where most values in a distribution fall. You can measure it using the mean, median, and mode. For example, the mean height and weight of a sample of teenage girls is 1.51 m and 46.33 kg.
Measures of variability indicate how far the values spread out. Descriptive statistics for dispersion include the standard deviation, variance, range, and interquartile range. Larger values indicate your data points spread out further. For example, heights range from 1.33 m to 1.68 m, for a range of 0.33 m.
The descriptive statistics that describe distributions of values include numeric measures such as kurtosis and skewness. However, graphing distributions using a histogram or a bar chart is often more intuitive.
Click the links to learn more about how and when to use the various types of statistics.
Bivariate Statistics
Bivariate descriptive statistics assess two variables together to determine whether they correlate or change over time. Frequently, analysts present this type of descriptive statistic using correlation coefficients, scatterplots, boxplots, and time series plots.
For example, the correlation between the heights and weights in this sample is 0.705.
Descriptive Statistics Examples
Let’s work through an example to see how descriptive statistics can help you understand a dataset quickly!
I have a dataset containing the heights and weights of 88 13-year-old girls who participated in a research study I worked on. Download the Excel file that contains the data for this example: HeightWeight.
Here are the descriptive statistics for these data. Even if you know nothing about this group’s heights and weights, you’ll quickly get the picture!
| Height M | Weight kg | |
| Median | 1.51 | 46.33 |
| Standard Deviation | 0.008 | 1.180 |
| Maximum | 1.67 | 80.74 |
| Minimum | 1.33 | 29.26 |
| Correlation | 0.705 | |
The median height and weight are 1.51 m and 46.33 kg, both of which fall near the peak bars of their respective histograms. These descriptive statistics indicate that most girls in the sample fall near these typical values. The minimum and maximum values along each horizontal x-axis indicates how far the values spread.
Additionally, the histograms indicate that heights follow a roughly symmetrical distribution where height frequencies taper off similarly in both directions from the peak bar. On the other hand, the distribution of weights is right-skewed. Most weights occur in the lower portion of the range and taper off more slowly as you move to the right.
The scatterplot illustrates the positive correlation in the table (0.705). As height increases, weight tends to increase.
Finally, between the table and the graphs, this descriptive statistics example allows you to understand the sample at a glance. You know which values are typical and unusual, the shape of these distributions, and the relationship between the variables.
Learn how to assess descriptive statistics using Excel.
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