# 2.1:
#
data = c( 72, 72, 66, 67, 68, 71 )
print( c( mean(data), diff(range(data)), sd(data) ) )


# 2.2:
#
data = c( 0.2508, 0.2510, 0.2506, 0.2509, 0.2506 )
print( c( mean(data), diff(range(data)), sd(data) ) )


# 2.3:
#
data = c( 142, 142, 143, 140, 135 )
print( c( mean(data), diff(range(data)), sd(data) ) )


# 2.4:
#
data = c( 0.2508, 0.2510, 0.2506, 0.2509, 0.2506 )
print( c( mean(data), diff(range(data)), sd(data) ) )


# 2.5:
#
data = c( 50, 35, 36 )
print( c( mean(data), diff(range(data)), sd(data) ) )


# 2.6:
#
data = c( 2, 8, 3, 3, 7, 1 )
print( c( mean(data), diff(range(data)), sd(data) ) )

# 2.7:
#
data = c( 2.5037, 2.5032, 2.5042 )
print( c( mean(data), diff(range(data)), sd(data) ) )


# 2.8:
#
data = c( 0.94, 0.89, 0.98, 0.87 )
print( c( mean(data), diff(range(data)), sd(data) ) )


# 2.9:
#
source('chap_2_prob_9_data.R')
hist_breaks = seq( 0, 100, by=10 )
h = hist( data, breaks=hist_breaks, freq=TRUE )
plot(h)
abline(v=100, col='red')


# 2.10:
#
source('chap_2_prob_10_data.R')
hist_breaks = seq( 60, 100, by=2 )
h = hist( data, breaks=hist_breaks, freq=TRUE )
plot(h)
abline(v=c(70, 90), col='red')


# 2.13:
#
source('chap_2_prob_13_data.R')
n = sum( DF$frequency )
x_bar = sum( DF$value * DF$frequency ) / n
s = sqrt( ( n * sum( DF$value^2 * DF$frequency ) - sum( DF$value * DF$frequency )^2 ) / ( n*(n-1) ) )
print( c( x_bar, s ))


# 2.14:
#
source('chap_2_prob_14_data.R')
n = sum( DF$frequency )
x_bar = sum( DF$value * DF$frequency ) / n
s = sqrt( ( n * sum( DF$value^2 * DF$frequency ) - sum( DF$value * DF$frequency )^2 ) / ( n*(n-1) ) )
print( c( x_bar, s ) )


# 2.15:
#
source('chap_2_prob_15_data.R')
n = sum( DF$frequency )
x_bar = sum( DF$value * DF$frequency ) / n
s = sqrt( ( n * sum( DF$value^2 * DF$frequency ) - sum( DF$value * DF$frequency )^2 ) / ( n*(n-1) ) )
print( c( x_bar, s ) )


# 2.16:
#
data = c( 72, 72, 66, 67, 68, 71 )
spec = c( 66, 72 )
p_out_of_spec = sum( (data <= spec[1]) | (data >= spec[2]) ) / length(data)
print( p_out_of_spec )


# 2.17:
#
source('chap_2_prob_9_data.R')
max_allowed_value = 100
p_out_of_spec = sum( data >= max_allowed_value ) / length(data)
print( p_out_of_spec )


# 2.18:
#
source('chap_2_prob_10_data.R')
spec = c( 70, 90 )
n_out_of_spec = sum( (data <= spec[1]) | (data >= spec[2]) )
p_out_of_spec = n_out_of_spec / length(data)
print( c( n_out_of_spec, p_out_of_spec ))


# 2.19:
#
source('chap_2_prob_13_data.R')
spec = 2.505 + c( -1, +1 ) * 0.0030
n = sum(DF$frequency)
n_too_low = sum( (DF$value <= spec[1]) * DF$frequency )
n_too_high = sum( (DF$value >= spec[2]) * DF$frequency )
p_out_of_spec = ( n_too_low + n_too_high )/n

print( c( n_too_low, n_too_high, p_out_of_spec ) )


# 2.20:
#
source('chap_2_prob_14_data.R')
spec = c( 0.83, 0.84 )
n = sum(DF$frequency)
n_too_low = sum( (DF$value <= spec[1]) * DF$frequency )
n_too_high = sum( (DF$value >= spec[2]) * DF$frequency )
p_out_of_spec = ( n_too_low + n_too_high )/n

print( c( n_too_low, n_too_high, p_out_of_spec ) )


# 2.21:
#
source('chap_2_prob_15_data.R')
min_allowed_value = 50
n = sum(DF$frequency)
n_too_low = sum( (DF$value <= min_allowed_value) * DF$frequency )
p_out_of_spec = ( n_too_low )/n
print( c( n_too_low, p_out_of_spec ) )