Question

2. Make a data frame consisting of 20 and 10 columns. Each column j should consist of 20 values from a normal distribution with mean (i-1) and standard deviation 0.5j. For example, the third column should be normal(mean=2, sd=1.5). Using this data frame, do each of the following (using code, of course):
a. Find the mean and standard deviation for each column.
b. Write code that counts the number of columns for which the sample mean and sample standard deviation are within 20% of the values used to generate the data.
c. Write code that writes the columns from part b to a new data frame.
d. For each value in the new data frame, subtract its column mean and divide by the column standard deviation.

Solution using r and python

Answer 1

Solution using r

# Create matrix of order 20 by 10

M=matrix(rep(0,20*10),nrow=20,ncol=10)

for(j in 1:10){

M[,j]=rnorm(20,mean=j-1,sd=j*0.5)

}

a. Find the mean and standard deviation for each column.

#Find mean and stored in 21st row
M1=rbind(M,apply(M,2,mean))

#Find mean and stored in 22nd row

M1=rbind(M1,apply(M,2,sd))

b. Write code that counts the number of columns for which the sample mean and sample standard deviation are within 20% of the values used to generate the data.

count=0

for(j in 1:10){

mean=j-1

sd=j*0.5

mean1=0

if(M1[21,j]>0.8*mean & M1[21,j]<1.2*mean ){

mean1=1

}

sd1=0

if(M1[22,j]>0.8*sd & M1[22,j]<1.2*sd){

sd1=1

count=count+mean1*sd1

}

c. Write code that writes the columns from part b to a new data frame.

M2=M

d. For each value in the new data frame, subtract its column mean and divide by the column standard deviation.

for(j in 1:10){

M2[,j]=(M2[,j]-mean(M2[,j]))/sd(M2[,j])

}