# script for topic 7o  
#  
     # first do the problem the long way
     # get the midpoints and the frequencies
mid_p <- seq(15,57,7)+3.5
mid_p
freqs <- c(15,46,54, 25, 45, 74, 16)
freqs
     # find the total number of data values
num_x <- sum( freqs )
num_x     
     # get the sum of the midpoints times
     # the count (the value in freqs)
sum_x <- sum( mid_p * freqs)
sum_x
     # then the mean is sum_x/num_x
mu <- sum_x/num_x
mu
     # now to get the standard deviation
     # first create squares of the midpoints
mp_sq <- mid_p^2
mp_sq
     #  then find the sum of the products of 
     #  the mp_sq and the counts
sum_xsq <- sum( mp_sq * freqs)
sum_xsq
     # finally use the alternative formula 
     # to get the standard deviation
std_dev = sqrt( (sum_xsq - (sum_x^2)/num_x)/num_x)
std_dev
#
     # then there is the shorter way
     # assuming that we know the midpoints and
     # the frequencies  (lines 5-8 above )
     # just make the data values
x <- rep( mid_p, freqs )
head(x, 19)
tail(x, 19)
     # then just find the mean and 
     # standard deviation of x
mean( x )
source("../pop_sd.R")
pop_sd(x)
     # and if this was a sample
sd(x)
#
     # Then there is the much shorter way
     #  again assuming that we did lines 
     #  7 and 8
source("../get_from_table.R")
get_from_table( 15, 22, freqs)