## Descriptive Summary in R

### Introduction to Descriptive Summary in R

Statistics is a study of data: describing properties of data (descriptive statistics) and drawing conclusions about a population based on information in a sample (inferential statistics). In this article, we will discuss the computation of descriptive summary in R (Descriptive statistics in R Programming).

Example: Twenty elementary school children were asked if they live with both parents (B), father only (F), mother only (M), or someone else (S) and how many brothers has he. The responses of the children are as follows:

Consider the following computation is required. These computations are related to the Descriptive summary in R.

• Construct a frequency distribution table in r relative to the case of each one.
• Draw a bar and pie graphs of the frequency distribution for each category using the R code.

### Creating the Frequency Table in R

# Enter the data in the vector form
x <- c("M", "B", "B", "M", "F", "S", "B", "M", "F", "B", "B", "F", "B", "M", "M", "B", "B", "F", "B", "M")

# Creating the frequency table use Table command
tabx=table(x) ; tabx

# Output
x
B F M S
9 4 6 1 

### Draw a Bar Chart and Pie Chart from the Frequency Table

# Drawing the bar chart for the resulting table in Green color with main title, x label and y label

barplot(tabx, xlab = "x", ylab = "Frequency", main = "Sample of Twenty elementary school children ",col = "Green")

# Drawing the pie chart for the resulting table with main title.
pie(tabx, main = "Sample of Twenty elementary school children ")

### Descriptive Statistics for Air Quality Data

Consider the air quality data for computing numerical and graphical descriptive summary in R. The air quality data already exists in the R Datasets package.

attach(airquality)
# To choose the temperature degree only
Temperature = airquality[, 4]
hist(Temperature)

hist(Temperature, main="Maximum daily temperature at La Guardia Airport", xlab="Temperature in degrees Fahrenheit", xlim = c(50, 100), col="darkmagenta", freq=T)

h <- hist(Temperature, ylim = c(0,40))
text(h$mids, h$counts, labels=h$counts, adj=c(0.5, -0.5)) In the above histogram, the frequency of each bar is drawn at the top of each bar by using the text() function. Note that to change the number of classes or the interval, we should use the sequence function to divide the$range$,$Max$, and$Min$, into$n\$ using the function length.out=n+1

hist(Temperature, breaks = seq(min(Temperature), max(Temperature), length.out = 7))

### Median for Ungrouped Data

Numeric descriptive statistics such as median, mean, mode, and other summary statistics can be computed.

median(Temperature)
## Output 79
mean(Temperature)
summary(Temperature)

A customized function for the computation of the median can be created. For example

arithmetic.median <- function(xx){
modulo <- length(xx) %% 2
if (modulo == 0){
(sort(xx)[ceiling(length(xx)/2)] + sort(xx)[ceiling(1+length(xx)/2)])/2
} else{
sort(xx)[ceiling(length(xx)/2)]
}
}
arithmetic.median(Temperature)

### Computing Quartiles and IQR

The quantiles (Quartiles, Deciles, and Percentiles) can be computed using the function quantile() in R. The interquartile range (IQR) can also be computed using the iqr() function.

y = airquality[, 4]  # temperature variable

quantile(y)

quantile(y, probs = c(0.25,0.5,0.75))
quantile(y, probs = c(0.30,0.50,0.70,0.90))

IQR(y)

One can create a custom function for the computation of Quartiles and IQR. For example,

quart<- function(x) {
x <- sort(x)
n <- length(x)
m <- (n+1)/2
if (floor(m) != m) {
l <- m-1/2; u <- m+1/2
} else {
l <- m-1; u <- m+1
}
c(Q1 = median(x[1:l]),
Q3 = median(x[u:n]),
IQR = median(x[u:n])-median(x[1:l]))
}

quart(y)

### FAQs in R Language

1. How one can perform descriptive statistics in R Language?
2. Discuss the strategy of creating a frequency table in R.
3. How Pie Charts and Bar Charts can be drawn in R Language? Discuss the commands and important arguments.
4. What default function is used to compute the quartiles of a data set?
5. You are interested in computing the median for group and ungroup data in R. Write a customized R function.
6. Create a User-Defined function that can compute, Quaritles and IQR of the inputted data set.

https://itfeature.com

https://gmstat.com

## Some Descriptive Statistics in R: A Comprehensive R Tutorial

### Descriptive Statistics in R

There are numerous functions in the R language that are used to computer descriptive statistics. Here, we will consider the data mtcars to get descriptive statistics in R. You can use a dataset of your own choice. To learn about what are descriptive statistics, read the different posts from the Basic Statistics Section.

### Getting Dataset Information in R

Before performing any descriptive or inferential statistics, it is better to get some basic information about the data. It will help to understand the mode (type) of variables in the datasets.

# attach the mtcars datasets
attach(mtcars)

# data structure
str(mtcars)

You will see the dataset mtcars contains 32 observations and 11 variables.

It is also best to inspect the first and last rows of the dataset.

# for the first six rows

# for the last six rows
tail(mtcars)

### Getting Numerical Descriptive Statistics in R

To get a quick overview of the dataset, the summary( ) function can also be used. We can use the summary( ) function separately for each of the variables in the dataset.

summary(mtcars)
summary(mpg)
summary(gear)

Note that the summary( ) the function provides five-number summary statistics (minimum, first quartile, median, third quartile, and maximum) and an average value of the variable used as the argument. Note the difference between the output of the following code.

summary(cyl)
summary( factor(cyl) )

Remember that if for a certain variable, the datatype is defined or changed R will automatically choose an appropriate descriptive statistics in R. If categorical variables are defined as a factor, the summary( ) function will result in a frequency table.

Some other functions can be used instead of summary() function.

# average value
mean(mpg)
# median value
median(mpg)
# minimum value
min(mpg)
# maximum value
max(mpg)
# Quatiles, percentiles, deciles
quantile(mpg)
quantile(mpg, probs=c(10, 20, 30, 70, 90))
# variance and standard deviation
var(mpg)
sd(mpg)
# Inter-quartile range
IQR(mpg)
# Range
range(mpg)

### Creating a Frequency Table in R

We can produce a frequency table and a relative frequency table for any categorical variable.

freq <- table(cyl); freq
rf <- prop.table(freq)

barplot(freq)
barplot(rf)
pie(freq)
pie(rf)

### Creating a Contingency Table (Cross-Tabulation)

The contingency table can be used to summarize the relationship between two categorical variables. The xtab( ) or table( ) functions can be used to produce cross-tabulation (contingency table).

xtabs(~cyl + gear, data = mtcars)
table(cyl, gear)

### Finding a Correlation between Variables

The cor( ) function can be used to find the degree of relationship between variables using Pearson’s method.

cor(mpg, wt)

However, if variables are heavily skewed, the non-parametric method Spearman’s correlation can be used.

cor(mpg, wt, method = "spearman")

The scatter plot can be drawn using plot( ) a function.

plot(mpg ~ wt)

### FAQs about Descriptive Statistics in R

1. How to check the data types of different variables/columns in R?
2. What is the use of str() function in R?
3. What is the use of head() and tail() functions in R?
4. How numerical statistics of a variable or data set can be obtained in R?
5. What is the use of summary() function in R?
6. How summary() function can be used to perform descriptive statistics of a categorical variable in R?
7. How to produce a frequency table in R?
8. What is the use of xtab() function in R?
9. What is the use cor(), plot(), and pie() functions, explain with the help of examples.
10. What functions are used to compute, mean, median, standard deviation, variance, Quantiles, and IQR.

Learn more about plot( ) function: plot( ) function

Visit: Learn Basic Statistics