R Statistical Software Basics – Descriptive Statistics - Percentiles

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")

Percentiles

Assume that the elements in a data set are rank ordered from the smallest to the largest. The values that divide a rank-ordered set of elements into 100 equal parts are called percentiles.

An element having a percentile rank of P_i would have a greater value than i percent of all the elements in the set. Thus, the observation at the 50th percentile would be denoted P₅₀, and it would be greater than 50 percent of the observations in the set.

An observation at the 50th percentile would correspond to the median value in the set.

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

quantile(filename, c(.10,.20,.30,.40,.50,.60,.70,.80,.90,.95))

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

quantile(StatMarks$StatisticsMarks, c(.10,.20,.30,.40,.50,.60,.70,.80,.90,.95)) 

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,c(.10,.20,.30,.40,.50,.60,.70,.80,.90,.95))

 10%  20%  30%  40%  50%  60%  70%  80%  90%  95%

  56.8 66.0   71.0  73.0   75.0  78.0  80.0   81.2  91.1   97.0

10% of students scored upto 56.8 marks, 20% of students scored upto 66 marks, 30% scored upto 71 marks, 50% scored upto 75 marks, etc.

PERCENTILES - 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. 

Percentiles

Assume that the elements in a data set are rank ordered from the smallest to the largest. The values that divide a rank-ordered set of elements into 100 equal parts are called percentiles.

An element having a percentile rank of P_i would have a greater value than i percent of all the elements in the set. Thus, the observation at the 50th percentile would be denoted P₅₀, and it would be greater than 50 percent of the observations in the set.

An observation at the 50th percentile would correspond to the median value in the set.

=PERCENTILE(array,k)

Array     The array or range of data that defines relative standing.

K     The percentile value in the range 0 to 1, inclusive.

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

=PERCENTILE(A2:A101,0.3)  gives the 30^th percentile

=PERCENTILE(A2:A101,0.5) gives 50^th percentile or Median

This means that 30% (30 out of 100) of the scores are lower or equal to 71. 

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