Statistics

Descriptive statistics help "describe, show or summarize data in a meaningful way" (Laerd, n.d.). For example, the summary may help describe patterns in the data. Descriptive statistics do not, however, allow us to "make conclusions beyond the data we have analyzed or reach conclusions regarding any hypotheses we might have made." (Laerd, n.d.). Understanding the limitations of the data is just as important to describe the data. 

Descriptive statistics are important because it helps us organize and visualize the raw data. For example, some data sets may be very large in size and hard to explain looking through data points individually. Descriptive statistics enable us to present the data and allow for a simpler interpretation of the data. For example, if we had students' results of 1000 tests, we may be interested in descriptive statistics that describe the performance of those students. We would also be interested in the distribution or spread of the marks. Here are two examples of statistics that help describe data:

• Measures of central tendency: These statistics describe the central position of a frequency distribution for a group of data. The distribution arranges the scores from lowest to highest. The central position can be described through the mode, median, and mean. 
• Measures of spread: This describes how spread out the data is. For example, the mean score of our 1000 students may be 68 out of 100. Unless every student scored 68, measures of spread describe how far away from the mean scores could be. The range, quartiles, absolute deviation, variance, and standard deviation help describe the spread of the data.

Used in combination, descriptive statistics illustrate the data in a more complete way. For example, the mean of 68 out of 100 and the standard deviation of 0.8 reports that the students' scores had an average of 68%, and the data was not spread out very far. Which means most students scored around 68. The statistics can be complemented with graphical display to show the distribution and a summary of results and limitations.

Reference: Laerd statistics (n.d.). Descriptive and Inferential Statistics. https://statistics.laerd.com/statistical-guides/descriptive-inferential-statistics.php

Any measurement that includes all the data, is called a population. A population can be small or large, as long as it includes all the data of the group you are studying. For example, if your sample includes the grades of a specific course. Then all the students in that course would represent your population. Descriptive statistics applied to populations, like the mean or standard deviation, are called parameters. 

Often, access to the entire population is not feasible. For example, collecting data from everybody who has taken statistics. Thus, you can make inferences about the population by collecting a sample of students (e.g., 100 students). The measurement of a sample is called a statistic. Inferential statistics are techniques that approximate the population parameter through samples collected. Inferential statistics arise out of the fact that sampling naturally incurs sampling error and thus a sample is not expected to perfectly represent the population. Some methods of inferential statistics are (1) the estimation of parameter(s) and (2) testing of statistical hypotheses.

Reference: Laerd statistics (n.d.). Descriptive and Inferential Statistics. https://statistics.laerd.com/statistical-guides/descriptive-inferential-statistics.php

Statistics by Matthew Cheung. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.