Question

USE R CODE AND SHOW OUTPUT

APPLIED STATISTICS 2

1. Traditionally, the policy for students’ course grade, >=90, A; between 80 to 89, B, between 70 to 79, C; between 60-69, D; and F, if <60.

Now, suppose we use a new grade policy. We just to separate all students into four parts, with the first parts assigning grade A, second parts assigning grade B, then, C, then D (no F). We use the data RecordMath2526.txt to have a try for our new grading policy.

1. . In the record file, there is no students ID. Assign students ID by random number between 10000 to 99999. You can use the following R code to get this, which produce 20 random numbers between 10000 to 99999.

    ID<-sample(10000:99999, 20)

2. Use kmeans function to cluster students into four clusters, based on Exam1, Exam2, and Final score.

3. Produce a data file with students ID and their cluster number (1, 2, 3, 4).

4. (Optional). Convert the numbers (1, 2, 3, 4) into grades (A,B,C,D) or (D,C,B,A).

USE R CODE AND SHOW OUTPUT

APPLIED STATISTICS 2

RecordMath2526.txt

Index Gender Hw1     Hw2     Hw3     Exam1 Hw4     Exam2 Hw5     Hw6     Hw7     Final

1 F 9    6          8          60        7          82        10        10        9          69

2 M 10   10        10        94        9          98        10        10        8          91

3 M 9    10        8          79        9          55        10        6          8          43

4 F 10   9          9          91        8          88        10        9          8          84

5 F 9    8          9          71        9          97        10        9          9          89

6 F 9    9          7          64        9          87        10        9          9          58

7 M 9    9          9          55        7          59        10        6          0          68

8 M 9    10        7          71        10        70        10        8          10        59

9 M 8    10        9          81        10        100      10        10        9          98

10 F 9   9          7          76        6          58        10        5          8          50

11 F 10  6          7          69        5          55        10        4          8          47

12 F 9   5          4          46        7          72        10        6          7          78

13 M 9   9          10        71        9          85        10        8          7          67

14 M 8   9          8          60        10        71        10        8          10        75

15 M 10 9          10        71        10        93        10        9          9          67

16 F 9   10        8          70        7          80        10        10        8          83

17 F 9   10        9          72        7          89        10        9          9          78

18 M 10  10        10        80        10        94        10        9          10        71

19 F 10  10        9          66        9          78        10        6          8          83

20 F 8   9          7          78        6          81        9          7          8 84           

USE R CODE AND SHOW OUTPUT

APPLIED STATISTICS 2

Answer 1

R code

##### Cluster Analysis####

cluster_data <- read.csv(file.choose(),header=T) # read saved CSV file containing data
attach(cluster_data)

  
## First part #########
ID<-sample(10000:99999,20)
cluster_data_ID<-data.frame(cluster_data,ID)

head(cluster_data_ID) # To see top rows

## Extracting Exam1, Exam2 and Final column
cluster_data_ID.new<- cluster_data_ID[,c(6,8,12)]
cluster_data_ID.class<- cluster_data_ID[,"ID"]
head(cluster_data_ID.new)

## To nomalize the data
normalize <- function(x){
return ((x-min(x))/(max(x)-min(x)))
}

cluster_data_ID.new$Exam1<- normalize(cluster_data_ID.new$Exam1)
cluster_data_ID.new$Exam2<- normalize(cluster_data_ID.new$Exam2)
cluster_data_ID.new$Final<- normalize(cluster_data_ID.new$Final)

head(cluster_data_ID.new)

### K means clustering
result<- kmeans(cluster_data_ID.new,4) #aplly k-means algorithm with no. of centroids(k)=4
result$size # gives no. of records in each cluster

result$centers # gives value of cluster center datapoint value(4 centers for k=4)
result$cluster #gives cluster vector showing the custer where each record falls

# To produce data file with ID and Cluster number

clust_number<-result$cluster

data_file<-data.frame(cluster_data_ID.class,clust_number)

data_file