# Social Statistics for a Diverse Society

# Study Questions

**Chapter 5**

The student study site questions in Chapter 4 utilized data from the Latin American Migration Project, a collaborative research effort based at Princeton University and the University of Guadalajara, supported by the National Institute of Child Health and Human Development (NICHD) (http://lamp.opr.princeton.edu). In this chapter we employ the same data, but focus on calculating the appropriate measures of variability.

A random sample of respondents was drawn from three Latin American countries: Nicaragua, Guatemala, and Costa Rica. The variable if interest is the duration (in months) of stay in the United States during respondents' first migration to the United States.

Nicaragua: 4, 6, 6, 6, 12, 36, 36, 36, 36, 60, 72, 78, 96, 120, 126, 156, 162, 162, 186, 540

Guatemala: 1, 1, 12, 24, 24, 24, 36, 36, 42, 60, 78, 84, 102, 102, 102, 102,132, 144

Costa Rica: 12, 12, 12, 12, 14, 15, 15, 18, 18, 24, 36, 48, 66, 120, 150, 150, 174, 282, 288

- Begin by either calculating (or referring back to your work on the student study site questions in Chapter 4 if you completed it) the values of the mode, the median, and the mean for each of the above countries:

- Calculate the range for each of the three countries listed above.

- Nicaragua has the largest range of the three countries. Which measure of central tendency would this most likely affect?

- Does the range tend be an accurate measure of variability within a distribution? Why or why not?

- The Interquartile Range (IQR) is one alternative measure of variability to the range. How is this measure defined in Chapter 5?

- Following the set of conventions established in Chapter 5, calculate the value of the IQR for each of the three countries listed above.

- At this point, your answers to Questions #1-5 have provided you with enough information to construct a box plot. Select one of the countries of interest to you and construct a box plot. Your box plot should clearly show the following quantities: minimum value, maximum value, the first quartile (Q1), the third quartile (Q3), and the median.

- One way to think about a distribution of observations or scores is to imagine the values around the mean as "noise." The quantity that is often used to describe this "noise" is the variance. Calculate the variance for each of the three countries above.

- Of course, the variance is a difficult measure of variability to interpret. Often, researchers rely on the standard deviation. Calculate this quantity for each of the countries listed above.

- What is the interpretation of the standard deviation as it was introduced in Chapter 5?

- Considering your answers from #5, #7 and #8, summarize your findings about the variability in these three distributions.

- One measure of variability that we have yet to address in this set of questions is the Index of Qualitative Variation (IQV). In order to use this measure with the data from the Latin American Migration Project, it is necessary to recode our data into a smaller number of categories. Recode the data for each country into three categories: less than 1 year, between 1 year and 3 years, and greater than 3 years.

- The IQV is generally used with nominal level variables. However, it is still possible to calculate the IQV using ordinal level variable as we have here. Calculate the IQV for Nicaragua.

- How would you interpret your answer from Question #13?