The field of statistics is divided into two major divisions: descriptive and inferential. Each of these segments is important, offering different techniques that accomplish different objectives. Descriptive statistics describe what is going on in a population or data set. Inferential statistics, by contrast, allow scientists to take findings from a sample group and generalize them to a larger population. The two types of statistics have some important differences.

## Descriptive Statistics

Descriptive statistics is the type of statistics that probably springs to most people’s minds when they hear the word “statistics.” In this branch of statistics, the goal is to describe. Numerical measures are used to tell about features of a set of data. There are a number of items that belong in this portion of statistics, such as:

- The average, or measure of the center of a data set, consisting of the mean, median, mode, or midrange
- The spread of a data set, which can be measured with the range or standard deviation
- Overall descriptions of data such as the five number summary
- Measurements such as skewness and kurtosis
- The exploration of relationships and correlation between paired data
- The presentation of statistical results in graphical form

These measures are important and useful because they allow scientists to see patterns among data, and thus to make sense of that data. Descriptive statistics can only be used to describe the population or data set under study: The results cannot be generalized to any other group or population.

## Types of Descriptive Statistics

There are two kinds of descriptive statistics that social scientists use:

Measures of central tendency capture general trends within the data and are calculated and expressed as the mean, median, and mode. A mean tells scientists the mathematical average of all of a data set, such as the average age at first marriage; the median represents the middle of the data distribution, like the age that sits in the middle of the range of ages at which people first marry; and, the mode might be the most common age at which people first marry.

Measures of spread describe how the data are distributed and relate to each other, including:

- The range, the entire range of values present in a data set
- The frequency distribution, which defines how many times a particular value occurs within a data set
- Quartiles, subgroups formed within a data set when all values are divided into four equal parts across the range
- Mean absolute deviation, the average of how much each value deviates from the mean
- Variance, which illustrates how much of a spread exists in the data
- Standard deviation, which illustrates the spread of data relative to the mean

Measures of spread are often visually represented in tables, pie and bar charts, and histograms to aid in the understanding of the trends within the data.

## Inferential Statistics

Inferential statistics are produced through complex mathematical calculations that allow scientists to infer trends about a larger population based on a study of a sample taken from it. Scientists use inferential statistics to examine the relationships between variables within a sample and then make generalizations or predictions about how those variables will relate to a larger population.

It is usually impossible to examine each member of the population individually. So scientists choose a representative subset of the population, called a statistical sample, and from this analysis, they are able to say something about the population from which the sample came. There are two major divisions of inferential statistics:

- A confidence interval gives a range of values for an unknown parameter of the population by measuring a statistical sample. This is expressed in terms of an interval and the degree of confidence that the parameter is within the interval.
- Tests of significance or hypothesis testing where scientists make a claim about the population by analyzing a statistical sample. By design, there is some uncertainty in this process. This can be expressed in terms of a level of significance.

Techniques that social scientists use to examine the relationships between variables, and thereby to create inferential statistics, include linear regression analyses, logistic regression analyses, ANOVA, correlation analyses, structural equation modeling, and survival analysis. When conducting research using inferential statistics, scientists conduct a test of significance to determine whether they can generalize their results to a larger population. Common tests of significance include the chi-square and t-test. These tell scientists the probability that the results of their analysis of the sample are representative of the population as a whole.

## Descriptive vs. Inferential Statistics

Although descriptive statistics is helpful in learning things such as the spread and center of the data, nothing in descriptive statistics can be used to make any generalizations. In descriptive statistics, measurements such as the mean and standard deviation are stated as exact numbers.

Even though inferential statistics uses some similar calculations — such as the mean and standard deviation — the focus is different for inferential statistics. Inferential statistics start with a sample and then generalizes to a population. This information about a population is not stated as a number. Instead, scientists express these parameters as a range of potential numbers, along with a degree of confidence.