# Descriptive Analysis in R Programming

In Descriptive analysis, we are describing our data with the help of various representative methods like using charts, graphs, tables, excel files, etc. In the descriptive analysis, we describe our data in some manner and present it in a meaningful way so that it can be easily understood. Most of the time it is performed on small data sets and this analysis helps us a lot to predict some future trends based on the current findings. Some measures that are used to describe a data set are measures of central tendency and measures of variability or dispersion.

**Process of Descriptive Analysis**

- The measure of central tendency
- Measure of variability

## Measure of central tendency

It represents the whole set of data by a single value. It gives us the location of central points. There are three main measures of central tendency:

- Mean
- Mode
- Median

## Measure of variability

Measure of variability is known as the spread of data or how well is our data is distributed. The most common variability measures are:

- Range
- Variance
- Standard deviation

## Need of Descriptive Analysis

Descriptive Analysis helps us to understand our data and is a very important part of Machine Learning. This is due to Machine Learning being all about making predictions. On the other hand, statistics is all about drawing conclusions from data, which is a necessary initial step for Machine Learning. Let’s do this descriptive analysis in R.

## Descriptive Analysis in R

Descriptive analyses consist of describing simply the data using some summary statistics and graphics. Here, we’ll describe how to compute summary statistics using R software.

### Import your data into R:

Before doing any computation, first of all, we need to prepare our data, save our data in external .txt or .csv files and it’s a best practice to save the file in the current directory. After that import, your data into R as follow:

Get the csv file here.

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `,` ` ` `stringsAsFactors = F)` `# Print the first 6 rows` `print` `(` `head` `(myData))` |

**Output:**

Product Age Gender Education MaritalStatus Usage Fitness Income Miles 1 TM195 18 Male 14 Single 3 4 29562 112 2 TM195 19 Male 15 Single 2 3 31836 75 3 TM195 19 Female 14 Partnered 4 3 30699 66 4 TM195 19 Male 12 Single 3 3 32973 85 5 TM195 20 Male 13 Partnered 4 2 35247 47 6 TM195 20 Female 14 Partnered 3 3 32973 66

### R functions for computing descriptive analysis:

**Mean**

It is the sum of observations divided by the total number of observations. It is also defined as average which is the sum divided by count.

where n = number of terms

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `,` ` ` `stringsAsFactors = F)` `# Compute the mean value` `mean = ` `mean` `(myData$Age)` `print` `(mean)` |

**Output:**

[1] 28.78889

**Median**

It is the middle value of the data set. It splits the data into two halves. If the number of elements in the data set is odd then the center element is median and if it is even then the median would be the average of two central elements.

where n = number of terms

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `,` ` ` `stringsAsFactors = F)` `# Compute the median value` `median = ` `median` `(myData$Age)` `print` `(median)` |

**Output:**

[1] 26

**Mode**

It is the value that has the highest frequency in the given data set. The data set may have no mode if the frequency of all data points is the same. Also, we can have more than one mode if we encounter two or more data points having the same frequency.

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the library` `library` `(modeest)` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `,` ` ` `stringsAsFactors = F)` `# Compute the mode value` `mode = ` `mfv` `(myData$Age)` `print` `(mode)` |

**Output:**

[1] 25

**Range**

The range describes the difference between the largest and smallest data point in our data set. The bigger the range, the more is the spread of data and vice versa.

Range = Largest data value – smallest data value

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `,` ` ` `stringsAsFactors = F)` `# Calculate the maximum` `max = ` `max` `(myData$Age)` `# Calculate the minimum` `min = ` `min` `(myData$Age)` `# Calculate the range` `range = max - min` `cat` `(` `"Range is:\n"` `)` `print` `(range)` `# Alternate method to get min and max` `r = ` `range` `(myData$Age)` `print` `(r)` |

**Output:**

Range is: [1] 32 [1] 18 50

**Variance**

It is defined as an average squared deviation from the mean. It is being calculated by finding the difference between every data point and the average which is also known as the mean, squaring them, adding all of them, and then dividing by the number of data points present in our data set.

where,

N = number of terms

u = Mean

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `,` ` ` `stringsAsFactors = F)` `# Calculating variance` `variance = ` `var` `(myData$Age)` `print` `(variance)` |

**Output:**

[1] 48.21217

**Standard Deviation**

It is defined as the square root of the variance. It is being calculated by finding the Mean, then subtract each number from the Mean which is also known as average and square the result. Adding all the values and then divide by the no of terms followed the square root.

where,

N = number of terms

u = Mean

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `, stringsAsFactors = F)` `# Calculating Standard deviation` `std = ` `sd` `(myData$Age)` `print` `(std)` |

**Output:**

[1] 6.943498

## Some more R function used in Descriptive Analysis:

**Quartiles**

A quartile is a type of quantile. The first quartile (Q1), is defined as the middle number between the smallest number and the median of the data set, the second quartile (Q2) – the median of the given data set while the third quartile (Q3), is the middle number between the median and the largest value of the data set.

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `, stringsAsFactors = F)` `# Calculating Quartiles` `quartiles = ` `quantile` `(myData$Age)` `print` `(quartiles)` |

**Output:**

0% 25% 50% 75% 100% 18 24 26 33 50

**Interquartile Range**

The interquartile range (IQR), also called as midspread or middle 50%, or technically H-spread is the difference between the third quartile (Q3) and the first quartile (Q1). It covers the center of the distribution and contains 50% of the observations.

IQR = Q3 – Q1

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `, stringsAsFactors = F)` `# Calculating IQR` `IQR = ` `IQR` `(myData$Age)` `print` `(IQR)` |

**Output:**

[1] 9

**summary() function in R**

The function **summary()** can be used to display several statistic summaries of either one variable or an entire data frame.

**Summary of a single variable:**

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `,` ` ` `stringsAsFactors = F)` `# Calculating summary` `summary = ` `summary` `(myData$Age)` `print` `(summary)` |

**Output:**

Min. 1st Qu. Median Mean 3rd Qu. Max. 18.00 24.00 26.00 28.79 33.00 50.00

**Summary of the data frame**

**Example:**

## R

`# R program to illustrate` `# Descriptive Analysis` `# Import the data using read.csv()` `myData = ` `read.csv` `(` `"CardioGoodFitness.csv"` `,` ` ` `stringsAsFactors = F)` `# Calculating summary` `summary = ` `summary` `(myData)` `print` `(summary)` |

**Output:**

Product Age Gender Education Length:180 Min. :18.00 Length:180 Min. :12.00 Class :character 1st Qu.:24.00 Class :character 1st Qu.:14.00 Mode :character Median :26.00 Mode :character Median :16.00 Mean :28.79 Mean :15.57 3rd Qu.:33.00 3rd Qu.:16.00 Max. :50.00 Max. :21.00 MaritalStatus Usage Fitness Income Miles Length:180 Min. :2.000 Min. :1.000 Min. : 29562 Min. : 21.0 Class :character 1st Qu.:3.000 1st Qu.:3.000 1st Qu.: 44059 1st Qu.: 66.0 Mode :character Median :3.000 Median :3.000 Median : 50597 Median : 94.0 Mean :3.456 Mean :3.311 Mean : 53720 Mean :103.2 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.: 58668 3rd Qu.:114.8 Max. :7.000 Max. :5.000 Max. :104581 Max. :360.0

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