title: "Problem Set 2 Part 2: R" output: pdf_document date: "2025-09-10" ---

{r setup, include=FALSE} knitr::opts_chunk$set(echo = T)

This part of the problem set involves the usage of R and the submission of R codes. Please fill in your R codes and answers in the indicated code chunks/areas. When finished, please knit the document to PDF and submit the PDF file to Moodle.

In the case that your document does not knit to PDF, this is the time to debug and ask me questions before the review. You may try the following:

1. Clear your local environment
2. Re-run all your cells in order and pay attention to whether you've defined variables after you called them.

Before we begin, we will need to load the necessary packages:

{r, message=FALSE} library(tidyverse)

\newpage

Measure of Dispersion: Mean Absolute Deviation

When we talk about the dispersion of a data set we are concerned with how spread out it is. Both standard deviation and IQR are measurements of dispersion. However, they are not the only measurements of dispersion.

One alternative statistic we can use is the mean absolute deviation. We can start from

$$ \bar X - X_i\,, $$

which is the deviation. Then the absolute deviation is

$$ |\bar x - x_i| $$

which takes the absolute value of $\bar x - x_i$. The mean absolute deviation is defined by taking the mean, which is

$$ \frac{\sum{i=1}^n |\bar x -xi|}{n}\,. $$

Suppose we have the following data set:

{r} x <- c(2, 0, 6, 28, 19, 6)

Question 1

Write code to find the mean of x and save it in a variable called mean_x.

{r} ## Your code goes here mean_x <- mean(x)

Question 2

Find the vector $\bar x - \boldsymbol x$. (Note $\bar x$ is a scalar number and $\boldsymbol x$ is a vector. In R, you can subtract a scalar from a vector directly. Try x-1 and see what happens).

```{r}

Your code goes here

mean_x - x

```

Question 3

Use your codes from the previous question and find the absolute value to obtain $|\bar x - \boldsymbol x|$. In R, you can find the absolute value using the abs() function.

```{r}

Your code goes here

mean(abs(mean_x - x))

```

Question 4

Use your codes from the previous question and find

$$ \frac{\sum{i=1}^n |\bar x -xi|}{n}\,. $$

Note that the form of $\frac{\sumi yi}{n}$ is simply the arithmatic mean. So, you may consider using the mean() function.

```{r}

Your code goes here

mean(x, trim = 0, na.rm = F)

```

Real Data Application

Question 5

In the datasets folder on Moodle, download a dataset named food_access.csv. Load the dataset into R and name it food.

If you are using Jupyter Hub, put the dataset in the same folder as this notebook so that you can load the dataset directly by its name without using file.choose(). If you need help with the read_csv() function, use the ?read_csv command.

{r} ## Your code goes here library(tidyverse) food <- read.csv("food_access.csv")

Question 6

Filter the data using the State variable to include only observations from North Carolina. Name the output dataset Food again.

```{r}

Your code goes here

food <- food %>% filter(State == "North Carolina")

```

Question 7

Use your codes from Question 4 to the find the mean absolute deviation for the NUMGQTRS variable. (Note: To extract a column as a vector, use the df$column syntax.)

```{r}

Your code goes here

mean(abs(food$NUMGQTRS))

```

Question 8

Use the data dictionary for the dataset (named food_access_dictionary.csv on Moodle) to determine the meaning of the NUMGQTRS variable.

Your answer:

The amount of population residing in group quarters in each county of North Carolina).