# PRACTICE answers

# 1. Calculate the mean age.

mean(iqlead$AGE)

# 2. Calculate the mean age of the females.

mean(iqlead$AGE[iqlead$SEX==2])

# 3. Calculate the number of females.

length(iqlead$AGE[iqlead$SEX==2])

# 4. How many observations of the Wind variable are there in the airquality 
# dataset?

length(airquality$Wind)

# 5. Calculate the mean of the Wind variable in the airquality dataset (ignore 
# NA's if necessary)

mean(airquality$Wind)
mean(airquality$Wind,na.rm=T)  #There are no NA's, so either works.

# 6. Trim 5% of the of the observations from each end and calculate the trimmed
# mean of the Wind variable.

mean(airquality$Wind,trim=0.05)

# 7. Generate a histogram for the Wind variable in the airquality dataset.

hist(airquality$Wind)

# 8. Generate a histogram for the Wind variable in the airquality dataset but 
# only for the month of June (Month==6).

hist(airquality$Wind[airquality$Month==6])

# 9. Add the argument freq=F to either of your histograms.  What did this change
# on your histogram?

hist(airquality$Wind,freq=F)   # y-axis changes from frequencies to densities.

# 10. Re-run your histogram for the Wind variable in the airquality dataset.  
# Does the distribution look approximately normal?

hist(airquality$Wind) # Approximately bell shaped I suppose

# 11. Run qqnorm() and qqline() for the Wind variable in the airquality 
# dataset.

qqnorm(airquality$Wind)

qqline(airquality$Wind)

# 12. Create a vector of values selected randomly from a normal distribution 
# that has approximately the same mean and standard deviation as the Wind 
# variable in the airquality dataset.  Make the sample size the same as well.  
# Then generate a histogram and q qqplot with the qqline added for this data.

mean(airquality$Wind) # Mean of about 10
sd(airquality$Wind)  # Standard Deviation of about 3.5
length(airquality$Wind)  # 153 observations

mydata <- rnorm(153, mean=10, sd=3.5)
hist(mydata)
qqnorm(mydata)
qqline(mydata)

# 13. Run the summary() function on the airquality dataset.

summary(airquality)

# 14. Make boxplots of the Wind variable in the airquality dataset broken out 
# by Month.

boxplot(airquality$Wind~airquality$Month)

# 15. Run a t-test on the Wind variable for May and July, then one for July and
# August. What do you observe?

t.test(airquality$Wind[airquality$Month==5],airquality$Wind[airquality$Month == 7])

     # Seems to be a statisticaly significant difference in means.


t.test(airquality$Wind[airquality$Month==7],airquality$Wind[airquality$Month == 8])

     # Does not seem to be a statistically significant difference in means.