Unit 4 Homework_ Data Distributions

Unit 4 Homework: Data Distributions (42 points) Zander Guadalupe For this homework, we will use R built-in data. R comes with several built-in data sets related to the 50 states of the United States of America. Professor XU has combined these data sets into a single CSV file named “us_states.csv”. Below is a list of variables in this data: ● name: the full state names. ● abb: 2-letter abbreviations for the state names. ● region: the geographic region (Northeast, South, North Central, West) that each state belongs to. ● division: the geographic division (New England, Middle Atlantic, South Atlantic, East South Central, West South Central, East North Central, West North Central, Mountain, and Pacific) that each state belongs to. ● population: population estimate as of July 1, 1975. ● income: per capita income (1974). ● illiteracy: illiteracy (1970, percent of population). ● life_exp: life expectancy in years (1969–71). ● murder: murder and non-negligent manslaughter rate per 100,000 population (1976). ● hs_grad: percent high-school graduates (1970). ● frost: mean number of days with minimum temperature below freezing (1931–1960) in a capital or large city. ● area: land area in square miles. Exercise 1: Reviewing Variable Labels and Values (14 points) Let’s start by taking a look at the structure of the U.S. states dataset and what’s included in it. To do this, we use the str() command. Question 1. How many observations are there in this data set? How many variables? (2 points) 50 observations, 12 variables Question 2. Which variables are nominal? Which variables are interval or ratio? (12 points) Nominal: illiteracy, life_exp, murder, hs_grad Interval: population, income, frost, area

Exercise 2: Percentages in Tables and Charts (8 points) In class and in your readings, we’ve covered different measures of dispersion. The most basic is the percentage, which we can read from tables and from charts. In this exercise, we’ll go one step further to characterize the dispersion in a distribution. Here’s a frequency table for the variable geographic division in the U.S. states dataset, followed by one that reports on percentage and a bar chart. Question 1. What is the mode of geographic division, and what is the percentage of states that are located in this division? (4 points) Mountain and south Atlantic. 16% Question 2. Which geographic division includes the least number of states? What is the percentage of states that are located in this division? (2 points) Middle atlantic. 6% Question 3. How would you describe the distribution of geographic divisions in terms of dispersion? Low, medium, or high dispersion? Justify your answer. (2 points) I would say medium because all of the percentages seem to be around the same range. Exercise 3. Medians and Quartiles (10 points) The summary() command provides summary statistics on continuous/numeric variables and reports on the minimum and maximum, the quartiles, and the mean and median. Here we call this command for the variable income: We’ll pair this text output with a histogram of income so that we can visualize the shape of the distribution. Finally, we’ll also look at a boxplot for the same variable. You can do this by changing the geom_histogram argument in the command line to geom_boxplot . Because there is only one variable to examine here, R gives us a sideways rendering of the boxplot instead of an up and down one. Use all three pieces of information–the summary output, the histogram, and the boxplot to answer the questions in this section.

Students can choose any division, but they only receive points for good reasoning.) I would prefer to live in West North Central because the average income of this region is second largest which is good. Also it has lower standard deviation and the size of the box is small which means there is less income inequality and there are no outliers.