Question

The following table contains cholesterol levels of 32 people. Determine if the sample comes from a population that is normally distributed. Draw a histogram, identify potential outliers, and draw the normality plot.

160	200	172	196	170	181	190	185
210	180	162	184	185	212	186	182
260	175	203	181	190	203	184	193
199	160	210	204	198	188	201	190

Answer 1

Sol:

load the data a vector in R.

use mean,median functions to get the mean and median of sample.

use hist function in R to get the histogram.

qqnorm and qqline to get the normal probbaility plot.

use boxplot function to know whether outliers exists

Rcode is

cholesterollevels <- c(160,   200,   172   ,196   ,170,   181   ,190   ,185,
210   ,180,   162   ,184,   185   ,212,   186,   182,
260   ,175,   203,   181   ,190,   203,   184   ,193,
199   ,160   ,210,   204   ,198,   188   ,201,   190)
mean(cholesterollevels)
median(cholesterollevels)
hist(cholesterollevels)
qqnorm(cholesterollevels)
qqline(cholesterollevels)
boxplot(cholesterollevels,col="darkgreen",main="boxplot")
fivenum(cholesterollevels)

Output:

> mean(cholesterollevels)
[1] 190.4375

> median(cholesterollevels)
[1] 189

fivenum(cholesterollevels)
[1] 160.0 181.0 189.0 200.5 260.0

Intrepretation:

For the given sample

mean=190.4375

median=189

mean>median

distribution is positively skewed.

frm qqplot alos we can see that the sample point are not exactly conforms to straight line.

There are deviations and confroms to skewed distribution .

sample does not follow normal distribution

From box plt we get fivenumber summary as

minimum value=160

Q1=181.0

Q2=189.0

Q3= 200.5

maximum=260

There exists one outlier and is at 260