Assignment 18

The purpose of the following code is to calculate the Mean and Standard Deviation of the data set of human body temperatures.

data=read.delim("exer6_34.dat",header=TRUE)

class(data)

## [1] "data.frame"

"data.frame"

## [1] "data.frame"

head(data)

##   TEMP
## 1 98.0
## 2 98.8
## 3 98.2
## 4 97.8
## 5 98.4
## 6 99.0

data$TEMP

##  [1] 98.0 98.8 98.2 97.8 98.4 99.0 99.2 97.9 98.4 96.9 98.2 97.6 98.0 98.5
## [15] 99.0 97.0 97.7 98.3 98.8 97.7 98.4 97.4 98.8 98.2 98.5 97.6 98.4 98.2
## [29] 98.7 98.6 98.3 98.2 98.0 98.0 98.0 99.0 97.4 99.0 98.2 98.8 98.6 97.7
## [43] 98.6 98.8 98.0 98.0 98.0 98.0 98.8 98.6 99.3 97.1 97.0 98.8 97.0 97.0
## [57] 97.4 99.4 98.1 98.0 97.8 98.4 97.4 97.6 97.2 97.3 98.0 97.8 98.5 99.1
## [71] 98.7 98.6 98.4 98.6 98.2 97.3 98.6 98.2 97.2 97.2 99.3 97.4 97.4 98.6
## [85] 98.1 98.1 98.6 99.2 98.5 97.6 97.8 96.7 96.8

temp=data$TEMP

temp=sort(temp)
temp

##  [1] 96.7 96.8 96.9 97.0 97.0 97.0 97.0 97.1 97.2 97.2 97.2 97.3 97.3 97.4
## [15] 97.4 97.4 97.4 97.4 97.4 97.6 97.6 97.6 97.6 97.7 97.7 97.7 97.8 97.8
## [29] 97.8 97.8 97.9 98.0 98.0 98.0 98.0 98.0 98.0 98.0 98.0 98.0 98.0 98.0
## [43] 98.1 98.1 98.1 98.2 98.2 98.2 98.2 98.2 98.2 98.2 98.2 98.3 98.3 98.4
## [57] 98.4 98.4 98.4 98.4 98.4 98.5 98.5 98.5 98.5 98.6 98.6 98.6 98.6 98.6
## [71] 98.6 98.6 98.6 98.6 98.7 98.7 98.8 98.8 98.8 98.8 98.8 98.8 98.8 99.0
## [85] 99.0 99.0 99.0 99.1 99.2 99.2 99.3 99.3 99.4

xbar=mean(temp)
xbar

## [1] 98.12

sd=sd(temp)
sd

## [1] 0.6468

str(data)

## 'data.frame':    93 obs. of  1 variable:
##  $ TEMP: num  98 98.8 98.2 97.8 98.4 99 99.2 97.9 98.4 96.9 ...

hist(data$TEMP,breaks=12,
     col="lightblue",
     border="purple",
     labels=TRUE,
     xlab="Temperature",
     ylab="Frequency",
     main="Human Body Temperature")

pnorm(98.76,98.12,.64)-pnorm(97.48,98.12,.64)

## [1] 0.6827

pnorm(99.40,98.12,.64)-pnorm(96.84,98.12,.64)

## [1] 0.9545

pnorm(100.04,98.12,.64)-pnorm(96.20,98.12,.64)

## [1] 0.9973

6.34- (a) Sample Mean=98.12366 Sample Standard Deviation=.6467978

  (c) [xbar-sd,xbar+sd]= %68
      [xbar-2sd,xbar+2sd]= %95
      [xbar-3sd,xbar+3sd]= %99.7
      
  (d) The distribution for this data resembles a normal distribution because the freuquency drops on both sides of the mean equally.
  
  (e) Standard Score= (score-mean)/sd
      
                    =(98.6-98.12366)/.6467
      
                    =.73657
                    
  -The mean human body temperature is 98.12366