R Statistical Software Basics – Descriptive Statistics - Quartiles

The practice sheet titled StatisticMarks Data.csv downloaded from Link. – Download Sheet

About the Data Sheet - The data in this sheet is related to marks scored by 100 Students in a Statistical Test.

Based on the data, we will use R Software Statistical functions to analyze the descriptive statistics.

In the Data Sheet, we have Data from A2:A101, A1 being the header of the Data. I have stored the StatisticMarks.csv file in Working Directory on my Desktop.

setwd("C:/Users/Rajesh Prabhakar/Desktop/R")

For inputting or reading Data from “StatisticMarks.csv” file, R Command would be

StatMarks=read.csv("StatisticMarks.csv")

Quartiles

Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q₁, Q₂, and Q₃, respectively.

Note the relationship between quartiles and percentiles. Q₁ corresponds to P₂₅, Q₂ corresponds to P₅₀, Q₃ corresponds to P₇₅. Q₂ is the median value in the set.

In R Statistical Software, Quartiles & percentiles are represented by function called “quantile”

quantile(  )

In the Data Sheet, we have Data from A2:A101, A1 being the header of the Data titled StatisticsMarks. 

quantile(StatMarks$StatisticsMarks)

StatMarks is the name of the variable in which we stored the data followed by $ sign and column header of the Data i.e. StatisticsMarks.

Remember the title of the column should be exactly same including the large caps & small caps or else it will give error.

In R the file names, column headers and row headers should exactly match the same or else the function will give errors

The result of this function in R Console is

quantile(StatMarks$StatisticsMarks)

0%    25%    50%    75%   100%

25.00  69.75  75.00  80.00 100.00

The results highlights that 25% of students scored less than 69.75 marks, 25% to 50% students scored between 69.75 & 75.00, 50% to 75% of students scored between 75.00 & 80.00 and 75 to 100% students scored between 80.00 & 100.00 marks.

                                                                           

Quartiles - Descriptive Statistics using Microsoft Excel Statistical Functions

The practice sheet can be downloaded from Link. Statistics Marks Data - Download Sheet

About the Data Sheet - The data in this sheet is related to marks scored by 100 Students in a Statistical Test. 

Based on the data, we will use Microsoft Excel Statistical functions to analyse the descriptive statistics. 

In the Data Sheet, we have Data from A2:A101, A1 being the header of the Data. 

Quartiles

Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q₁, Q₂, and Q₃, respectively.

Note the relationship between quartiles and percentiles. Q₁ corresponds to P₂₅, Q₂ corresponds to P₅₀, Q₃ corresponds to P₇₅. Q₂ is the median value in the set.

Quartiles are mostly used in sales and survey data to divide populations into groups.

=QUARTILE(array,quart)

Array     is the array or cell range of numeric values for which you want the quartile value.

Quart     indicates which value to return.

Quartile = 0 returns Minimum Value

Quartile = 1 returns First Quartile (25^th   Percentile)

Quartile = 2 returns Second Quartile (50^th Percentile) = Median

Quartile = 3 returns Third Quartile (75^th Percentile)

Quartile = 4 returns Maximum Value

In the Data Sheet, we have Data from A2:A101, A1 being the header of the Data. 

=Quartile(A2:A101,0)

=Quartile(A2:A101,1)

=Quartile(A2:A101,2)

=Quartile(A2:A101,3)

=Quartile(A2:A101,4)

First Quartile i.e. 25% of students scored less than 69.75 Marks 

Second Quartile i.e. 25% of students scored between 69.75 to 75 Marks 

Third Quartile i.e. 25% of students scored between 75 & 80 Marks 

Fourth Quartile i.e. 25% of students scored between 80 & maximum 100 Marks.

Minimum Marks scored in test is 25

Result is below Table

The practice sheet can be downloaded from Link. Statistics Marks Data - Download Sheet