Question

The following data were drawn 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). 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

a) What is the level of measurement of duration of stay during first U.S. migration?

b) Calculate the value of the mode for each country.

c) How does the mode for Guatemala compare to that of Costa Rica?

d) In light of your answer to c), perhaps one explanation is that respondents from Latin American countries that are closer to the United States have a higher modal duration of stay in the United States during their first U.S. migration than respondents from Latin American countries that are further away from the United States. Does the evidence from Nicaragua support this idea? (Hint: examine a map of Latin America to see whether you would expect the mode for Nicaragua to be greater than or less than that for Costa Rica and Guatemala.)

e) Given your results from b), you are interested in extending this idea to the value of the median. Which country would you expect to have the highest median duration of stay in the United States during first U.S. migration?

f) Calculate the value of the median for each country. Which of the three countries above in fact has the highest median value? Does this support your idea that respondents from Latin American countries that are closer to the United States have a higher median duration of stay in the United States during their first U.S. migration than respondents from Latin American countries that are further away from the United States? Explain.

g) Notice that both Guatemala and Costa Rica have some very low and very high values. Which measure of central tendency is most susceptible to such extreme values?

h) Given your results from b) and f), you are interested in extending the idea that respondents from Latin American countries that are closer to the United States have a higher mean duration of stay in the United States during their first U.S. migration than respondents from Latin American countries that are further away from the United States. Which country would you expect to have the lowest mean duration of stay during first U.S. migration?

i) Calculate the value of the mean for each country. Which of the three countries above in fact has the lowest mean duration? Does this support your idea that respondents from Latin American countries that are closer to the United States have a higher mean duration of stay in the United States during their first U.S. migration than respondents from Latin American countries that are further away from the United States? Explain.

j) For each country, identify the direction in which (if any) the distribution is skewed? Provide specific evidence using your answers from the previous questions.

Answer 1

a)

The variable of interest is the duration of stay which is measured in months.

level of measurement:  Ratio level of measurement. Since the data values are measured in number (quantitative in nature) and the distance between two measurements is defined by month (fixed distance in terms of the month with zero as a base point), this is a ratio level of measurement.

b)

The mode value is obtained in excel. The screenshot is shown below,

c)

The mode value for the country of Guatemala is too larger compared to Costa Rica.

d)

If we see the map, the distance and the duration of stay from the US is in the following order

Distance (descending): Guatemala > Nicaragua > Costa Rica

Mode for the duration of stay(descending): Guatemala > Nicaragua > Costa Rica

Both are in the same order hence we can say the explanation supported.

e)

If we apply the same explanation as above to the median value, Guatemala should have the highest median value among three

f)

The median value is obtained in excel. the screenshot is shown below,

Nicaragua has the highest median value

This evidence doesn't support the idea.

g)

The mean value is affected most by an outlier compared to the median and mode.

h)

If we follow the same explanation, the mean should be in the following order

mean(descending): Guatemala > Nicaragua > Costa Rica

i)

The mean value is obtained in excel. the screenshot is shown below,

Order (descending):  Nicaragua > Costa Rica > Guatemala

This evidence doesn't support the idea.

j)

For each country, the mean value is greater than the median value

	mean		median
Nicaragua	96.8	>	66
Guatemala	61.44444	>	51

hence the distribution of duration of stay for each country is skewed to right (positively skewed)