## Descriptive Statistics

This topic explains what statistics are, and how they can be useful to public policy and management professionals. This topic teaches students about different levels of measurement, the differences between descriptive and inferential statistics, and the relationships between overall populations and samples from which statistics are drawn. This topic also teaches students about different ways to summarize basic descriptive statistics, including percentages and proportions, ratios and rates, frequency distributions and graphs and figures.

**Topic Learning Outcome**: Upon mastering this topic at the MPP/MPA level, the student will understand the differences between descriptive and inferential statistics as well as the relationships between overall populations and samples from which statistics are drawn. The student will understand the main ways in which descriptive statistics can be summarized -- including percentages and proportions, ratios, rates, and frequency distributions as well as graphs and figures -- and will be able to describe and apply the core concepts listed below.

**Core Concepts associated with this Topic**: Data Set, Frequency Distribution; Variance; Standard Deviation; Variable; Statistical Spread (Dispersion).

**Recommended Reading**

*Harvard: API-201 Quantitative Analysis and Empirical Methods*

Moore, David S., George P. McCabe, and Bruce Craig. 2014. “Introduction to the Practice of Statistics.” 8th Edition. Sections 1.1, 2.1, 1.2, 2.2, 2.6.

Schwabish, Jonathan A. 2014. "An Economist's Guide to Visualizing Data." *Journal of Economic Perspectives*, 28(1): 209-34.

*Wagner: GP.1011 Statistical Methods for Public, Nonprofit, and Health Management*

Healey, Joseph F. 2013. “The Essentials of Statistics: A Tool for Social Research.” 3^{rd} edition. Wadsworth/Cengage Learning. Chapters 1 and 2.

Blustein, J. “SPSS: The Wagner Way.” Chapter 1.

*George Washington: PPPA 6002 Research Methods and Applied Statistics*

De Veaux, Richard, Paul Velleman, and David Bock. “Intro Stats.” 4th edition. Pearson. Chapters 1-4.

*American: PUAD 605 Quantitative Methods for Public Managers*

Healey, J.H. 2011. “Statistics. A tool for social research.” 9th Edition. Thompson, Wadsworth. Chapters 1 – 4.

*UCLA: PUB PLC 203 Statistical Methods for Public Policy I*

De Veaux, Richard D., Paul F. Velleman, and David E. Bock. 2011. “Stats: Data and Models.”* *3rd Edition. Boston: Pearson Education. Chapters 4-5.

*Rutgers: 34:833:530 Analytical Methods*

Wang, Xiaohu. 2010. “Performance Analysis for Public and Nonprofit Organizations.” Jones and Bartlett Publishers. Chapter 14.

**Sample Assessment Questions:**

1) Define the following terms: Data Set; Frequency Distribution; Variance; Standard Deviation; Variable; Statistical Spread (Dispersion).

2) Create a graph or figure to illustrate an interesting set of statistics that may be useful for policymakers to understand.

3) What are the differences between descriptive and inferential statistics?

4) Consider the following three data sets A, B and C.

A = {9,10,11,7,13}

B = {10,10,10,10,10}

C = {1,1,10,19,19}

a) Calculate the mean of each data set.

b) Calculate the standard deviation of each data set.

c) Which set has the largest standard deviation?

d) Is it possible to answer question c) without calculations of the standard deviation?

[Question 4 comes from Free Math Tutorials at http://www.analyzemath.com/statistics/mean.html, accessed 5 February 2015.]

**Page created by** Sean Goertzen, last edited by Ian Clark on 5 February 2015.