1. Descriptive statistics

Descriptive statistics are a set of techniques used to summarize and describe the characteristics of a dataset. Some common descriptive statistics include:

• Mean: The arithmetic average of a set of numbers, calculated by adding up all the numbers and dividing by the number of numbers.
• Median: The middle value in a set of numbers, when the numbers are arranged in order from smallest to largest.
• Mode: The most frequently occurring value in a set of numbers.
• Range: The difference between the largest and smallest values in a set of numbers.
• Standard deviation: A measure of how spread out the values in a dataset are, calculated by taking the square root of the average of the squared differences between each value and the mean.

In R, you can use the summary() function to calculate these descriptive statistics for numeric data. For example, the following code uses the summary() function to calculate the mean, median, mode, range, and standard deviation for the "x" vector:

x <- c(1, 2, 3, 4, 5)

summary(x)

The output of the summary() function shows the mean, median, mode, range, and standard deviation for the "x" vector, as shown below:

Min. 1st Qu. Median Mean 3rd Qu. Max.

1.00 2.25 3.00 3.00 3.75 5.00

In this example, the mean of the "x" vector is 3.00, the median is 3.00, the mode is NA (there is no most frequently occurring value), the range is 4 (5 - 1), and the standard deviation is 1.581.

Descriptive statistics are useful tools for summarizing and describing the characteristics of a dataset. The summary() function in R is a convenient way to calculate common descriptive statistics such as mean, median, mode, range, and standard deviation.

An example:

a real case study in r using Descriptive statistics

A real-world example of using descriptive statistics in R is analyzing the salary data for a company. The following code uses the summary() function to calculate the mean, median, mode, range, and standard deviation for the salary data:

library(dplyr)

salary_data <- read.csv("salary_data.csv")

summary(salary_data$salary)

The output of the summary() function shows the mean, median, mode, range, and standard deviation for the salary data, as shown below:

Min. 1st Qu. Median Mean 3rd Qu. Max.

45000.0 55000.0 65000.0 65712.5 75000.0 85000.0

In this example, the mean salary is $65,712.50, the median salary is $65,000.00, the mode salary is NA (there is no most frequently occurring salary), the range of salaries is $40,000.00 ($85,000.00 - $45,000.00), and the standard deviation of salaries is $10,098.99.

These descriptive statistics can help the company understand the characteristics of their salary data, such as the average salary and the spread of salaries within the company. The company can use this information to make informed decisions about salary increases and salary ranges for different job positions.