high_temps<-c(90, 87, 89, 90, 88, 86, 91, 89, 88, 85, 83, 88, 80, 83, 87, 89, 89, 91, 93, 92, 92, 92, 76, 79, 78, 75, 79, 85, 83, 88, 86)
#
# the functon mean() calculates the mean (i.e. average)
# of the vector values 
#
ave <- mean(high_temps)
ave
#
# the median() function calculates the central value 
# of the temperatures if the are ordered (sorted)
#
middle <- median(high_temps)
middle
#
# the sd() function calculates the standard deviation 
# it coincides with what Excel calls stdev.s (the sample version)
#
stdev <- sd(high_temps)
stdev
#
# the min() function determines the lowest value
#
least <- min(high_temps)
least
#
# the max() function determines the highest value
#
most <- max(high_temps)
most
#
# the quantile() function can be used to obtain 
# the first quartile 
# note the R function has an "n" as opposed to an "r"
#
first_quartile <- quantile(high_temps, 0.25)
first_quartile
#
# the quantile() function can be used to obtain 
# the third quartile 
#
third_quartile <- quantile(high_temps, 0.75)
third_quartile
#
# the summary() function is a fast way to obtain
# many of the above statistics
#
high_temps_summary <- summary(high_temps)
high_temps_summary
#
# we can use the sort() function to put the temperatures 
# in order from lowest to highest
#
sorted_high_temps <- sort(high_temps)
sorted_high_temps
#
# then the second smallest temperature has an 
# index of 2 
#
second_smallest <- sorted_high_temps[2]
second_smallest
#
# length determines the size of the vector which 
# in this case is the number of temperatures (or days)
#
sample_size = length(high_temps)
sample_size
#
# the second largest has an index of the length minus one
#
second_largest <- sorted_high_temps[sample_size -1]
second_largest 
#
# use hist() to make a fast histogram of the data
#
hist(high_temps)
#
# use boxplot() to make a fast"box and whiskers" plot
#
boxplot(high_temps)
#
# boxplot.stats tells us 
# stats: min | 1st-quart | median | 3rd-quart | max
# n: sample size
# conf: a range based on the inter-quartile range and sample size
# Out: list any outliers -- non here
#
boxplot.stats(high_temps)