R would be chosen over other languages for a data analysis project because of its rich library support for statistical analysis and data visualization. R's extensive set of packages makes it a better fit for data-centric tasks as compared to tasks like website or mobile app development.

To calculate the mean of each numeric variable in a data frame in R, you can use the sapply() or lapply() function to apply the mean() function to the subset of numeric variables. This approach allows you to calculate the mean for each numeric variable individually.

In R, the <- operator is commonly used to assign a value to a variable. For example, x <- 5 assigns the value 5 to the variable x. The = operator can also be used for assignment, but the <- operator is more commonly used.

Pie charts have the advantage of being easy to understand and visually appealing, making them suitable for displaying proportions. However, they have disadvantages such as being limited to a few categories, making it difficult to compare values accurately. Additionally, pie charts may not be suitable for showing hierarchical data or dealing with whole numbers, and they can be space-consuming. The choice of using a pie chart depends on the specific data and the purpose of visualization.

Some potential risks or downsides of using global variables in R include difficulty in tracking and managing dependencies between functions, increased potential for naming conflicts if multiple global variables have the same name, and reduced code modularity and reusability since functions become dependent on specific global variables. It is important to carefully manage and control the usage of global variables to minimize these risks.

Functions like subset(), filter(), and mutate() are specifically designed to operate on data frames in R. They allow for data manipulation, subsetting, and creating new variables within a data frame.

Starting with the installation of R and RStudio, the basics of R programming should be the first focus. Online resources, such as free tutorials, R documentation, or forums like Stack Overflow can be incredibly helpful. A mix of hands-on practice and theoretical learning usually works best.

All of the mentioned scenarios may require handling missing values when calculating the median in R. For example, when analyzing survey data, it's common to have missing responses that need to be handled appropriately. Similarly, when calculating the median income, missing income values should be accounted for. Handling missing values ensures accurate median calculations and prevents biased results.

In R, you can define a custom function called customMode() (or any preferred name) to calculate the mode of a numeric vector. This allows you to implement your own logic for identifying the mode based on the frequency of values.

The concept of performing operations on entire vectors at once, without the need for looping over individual elements, is known as vectorization in R. It leverages optimized internal functions in R to apply operations to entire vectors efficiently, resulting in concise and computationally efficient code.