# Descriptive and Inferential Statistics

What are the main differences between descriptive and inferential statistics? Give examples of each.

When would random sampling not be the best approach to sample selection? Give an example.

© BrainMass Inc. brainmass.com October 9, 2019, 7:58 pm ad1c9bdddfhttps://brainmass.com/statistics/descriptive-statistics/descriptive-and-inferential-statistics-135024

#### Solution Preview

1. What are the main differences between descriptive and inferential statistics? Give examples of each.

Whereas descriptive statistics simply describe what's going on in the data e.g., frequency of traffic accidents, or the percentage or average number of murders each month, etc. inferential statistics are interested in making inferences from the data. e.g., why there are more accidents on Friday than on Monday and is this pattern similar across difference areas and regions?

Descriptive statistics deals with answering questions about a certain set of data. "What does the data look like?" It communicates the gist of a set of data to a second party. Descriptive statistics enables someone to summarize data in a concise manner. It enables someone to describe the data without having to provide a lengthy explanation. http://library.thinkquest.org/C0122162/basics.htm

Thus, Descriptive Statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. Descriptive statistics are typically distinguished from inferential statistics. Descriptive Statistics are used to present quantitative descriptions in a manageable form. In a research study we may have lots of measures. Or we may measure a large number of people on any measure. Descriptive statistics help us to simply large amounts of data in a sensible way. Each descriptive statistic reduces lots of data into a simpler summary. It can be described using the following measures:

1. Mode

The mode in a list of numbers is the number that occurs most often, if such a number exists.

2. Median

The median of a list of numbers is found by ordering them from least to greatest. If the list has an odd number of numbers, the middle number in this ordering is the median. If there is an even number of numbers, the median is the sum of the two middle numbers, divided by 2. Note that there are always as many numbers greater than or equal to the median in the list as there are less than or equal to the median in the list.

3. Mean

The mean of a list of numbers is also called the numerical average. It is found by adding all the numbers in a list and dividing by the number of numbers in the list. http://library.thinkquest.org/C0122162/basics.htm

EXAMPLE OF DESCRIPTIVE STATISTICS:

For instance, consider a simple number used to summarize how well a batter is performing in baseball, the batting average. This ...

#### Solution Summary

By discussion and examples, this solution answers the questions: What are the main differences between descriptive and inferential statistics? When would random sampling not be the best approach to sample selection?